-14 Points DETAILS LARCALC11 7. about the x-axis. Get the free "Solids of Revolutions - Volume" widget for your website, blog, Wordpress, Blogger, or iGoogle. 1 POINT Select the best method to find the volume of a solid of revolution generated by revolving the region bounded by the graph of y -x2 x and the x-axis around the line y -19. Con x&178; The volume of the solid generated by revolving the region between y 4x and y about the x-axis is 241. (Type an exact answer, using as needed). Question Use the disk method or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line. Jan 17, 2019 Use the shell method to find the volume of the solid generated by revolving the region bounded by the line y 3x 4 y 3 x 4 and the parabola y x2 y x 2 about the x-axis. 3 Find the volume of a solid of revolution with a cavity using the washer method. Method 1 Rotating this shape about x6 will produce a conical frutsum. and l l is the length of the slant of. y 6x2 y 0 x 2 a. Please be explicit because I have no clue how to use the shell method. In the case of a right circular cylinder (soup can), this becomes V r2h. Volumes - Cylindrical Shell. How do you find the volume of the solid generated by revolving the region bounded by the lines and curves about the x-axis ye(-x), y0, x0, x1 Calculus Applications of Definite Integrals Determining the Volume of a Solid of Revolution. 1 is an example of a cylinder with a noncircular base. Question Help 6. The volume is (Type an exact answer, using a as needed. Observing the given function yields. In other words, it will be the volume of the cone with base radius 6 and height 6 (as defined by the lines yx and. Find the volume of the solid generated by revolving the region bounded by the given line and curve about the x-axis. 1, 3. Find more Mathematics widgets in WolframAlpha. (Round your answers to three decimal places. ) YA 4 8 y2x R y 8 yx. How do you find the volume of the solid generated by revolving the region bounded by the graphs y1x, y0, x1, x4, about the x axis Calculus Applications of Definite Integrals Determining the Volume of a Solid of Revolution. ) Use the region in the first quadrant bounded by the axis and the graph of x(5-x). 6. And I end up with the following integral. Surface area of solid. Expert-verified. The line y 1 a. Finding the volume of a solid revolution is a method of calculating the volume of a 3D object formed by a rotated area of a 2D space. ) There are 2 steps to solve this one. and taking the difference, or (c) using shell integration (rotating. By Washer Method, the volume of the solid of revolution can be expressed as V r r(r2 x2 R)2 (r2 x2 R)2dx, which simplifies to V 4R r rr2 x2dx. required to find these two intersection values. Answer link. ) In each case, nd the volume of the solid generated by revolving the shaded region about the given axis. Find the volume of the solid generated by revolving the region bounded by y 4x 3 and the xaxis in the interval 2, 4. ) Find the volume of a solid of revolution generated by revolving this region about the line x 9. Find the volume of the solid generated by revolving the region about the given axis. Advanced Math. Use the procedure. Question Find the volume of the solid generated by revolving the region bounded by the graphs of y 2x2 1 and y 2x 10 about the x-axis. This can be done b. There are 3 steps to solve this one. Multiplying the height, width, and depth of the plate, we get. When we use the slicing method with solids of revolution, it is often called the disk method because, for solids of revolution, the slices used to over approximate the volume of the solid are disks. Finding the volume. The volume of the resulting solid is (Type an exact answer. dx -3 (Type exact answers. 1 Answer Frederico Guizini S. V approx 0. Use the disk method to find the volume of the solid of revolution generated by rotating the region between the graph of f (x) x f (x) x and the x-axis x -axis over the interval 1,4 1, 4 around the x-axis. The region in the first quadrant bounded above by the parabola y 3x2, below by the x-axis, and on the right by the line x 2. If we let f (x) x according to formula 1 above, the volume is given by the definite integral. First graph the region R and the associated solid of revolution, as shown in Figure 6. Answer Since were revolving about the x-axis, we need to integrate with respect to y (using the shell method). Show Solution. Find the volume of a solid of revolution formed by revolving the region bounded above by (f(x)4x) and below by the (x)-axis over the interval (0,4) around the line (y2. the line y 4 b. Question Find the volume of the solid generated by revolving the following region about the given axis. (Type an exact answer, using as needed). (a) Find the area of R. Find the volume of a solid of revolution generated by revolving this. Added Apr 30, 2016 by dannymntya in Mathematics. Find the volume of the solid generated by revolving the area bounded by the given curves about the indicated axis of revolution. (c) the line. Feb 18, 2022 When we use the slicing method with solids of revolution, it is often called the disk method because, for solids of revolution, the slices used to over approximate the volume of the solid are disks. Now put x x in terms of y y so that we can integrate along y y x y 3 x y 3. ) AY y21021 8. Its volume is calculated by the formula Our online calculator, based on Wolfram Alpha system is able to find the volume of solid of revolution, given almost any function. Using the shell method, set up the integral to find the volume of the solid generated by rotating the region bounded by yx and y 6x about the x. Compute the volume of the solid generated by revolving the region bounded by y 5x and y x2 about each coordinate axis using the methods below. Use the disk method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. The volume is 107. x5y2,x0, between y5 and y5 1250 25n 330 100 150 None of the other choices. X tan 0. Example Using the Disk Method to Find the Volume of a Solid of Revolution 1. Open in App. At each point located on the graph, the cross-section of the solid, parallel to the y-axis, will be a circle of radius y. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y 4. The slice is taken at some value of x and has thickness dx. The volume of the solid generated by revolving the region between y 5 Squareroot x y x22 about the x-axis is 507. Solution we have to find the volume generated by revolving the region about the x axis. (Type an exact answer, using and radicals as needed, or type the answer as a decimal rounded to the nearest tenth. Here is the region we are rotating about the x-axis. ISBN 9781337614085. Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y ex and the line x ln 8 about the line x ln 8. We can extend the disk method to find the volume of a hollow solid of revolution. y e x, y 0, x 0, x. Type an exact answer, using t as needed. Find the volume of the solid generated by revolving the triangular region bounded by the curve y 4x3 and the lines x 1 and y 12 about the y-axis. Con x The volume of the solid generated by revolving the region between y 4x and y about the x-axis is 241. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Nov 10, 2020 For each of the following problems, select the best method to find the volume of a solid of revolution generated by revolving the given region around the &92;(x&92;)-axis, and set up the integral to find the volume (do not evaluate the integral). y ex, y 0, x 0 (a) Find the area of the region. Expert Answer. Find the volume of the solid generated by revolving the following region about the y-axis. Question Sketch the region bounded by the curves y2x3,y2 and x0 then find the volume of the solid generated by revolving this region about the x-axis. This problem has been solved You&39;ll get a detailed solution from a subject matter expert that helps you learn core concepts. volume of the solid formed by revolving the region bound by yx and yx2 about the y axis. ) AY y21021 8. a) 41 pi b) 46 pi c) 42 pi d) 44 pi e) 45 pi. Volumes by the Disk Method About the x-axis About the y-axis 3y 2y 2 About the y-axis About the x-axis y sin x cos x x tan. V (Type exact answers, using a as needed. Find the volume of the solid generated by revolving the triangular region bounded by the curve y 4x3 and the lines x 1 and y 12 about the y-axis. Sorted by 0. Having trouble with this question from my OpenStax Calculus Volume 1 Homework, It is question 89 of Chapter 6 about Solid Revolution. Question Use the disk method or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line. Find the volume of the solid generated by revolving the region bounded by y 3, x 3 and x 3y2 about the x-axis. Question Find the volume of the solid generated by revolving the region bounded by the given line and curve about the x-axis. How do you find the volume of the solid generated by revolving the region bounded by the graph. The procedure is essentially the same, but now we are dealing. c2 (x 2c sinh (2xc)) (b) Determine the volume of solid generated by revolving the plane area bounded by y 2 4x and x 4 about the line x 4. When this expression is revolved around x axis through 360 we have solids of revolution. y x2, y 4, x 0. Assuming that the functions and are continuous and non-negative on the interval and consider a region that is bounded by two curves and between and. This can be done b. simplify the algebra with u 1 x so we have. Volume of Solids in Revolution. Use the shell method to find the volume of the solid generated by revolving the region bounded by the line y 6x 7 and the parabola yx2 about the following lines. 13 we see a plane region under a curve and between two vertical lines (xa) and. (b) The area between the curve y x32 and the ordinates x 1 and x 3. Volume and Surfaces of Solid of Revolution (a) Find the volume of the solid generated by the revolution of an arc of the catenary y c cosh(xc) 2 about the x-axis. Use the disk method or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line. About the y-axis 20. dx -3 (Type exact answers. For example, in Figure 3. y 6x2 y 0 x 2 a. show all steps please thanks sketch the region bounded by the curves y5x, y0, and x2. Free volume of solid of revolution calculator - find volume of solid of revolution step-by-step. Find the volume of the solid generated by revolving the region bounded above by the line y 4 , below by the curve y x2 about a. dV (y2 2 y2 1)dx. To calculate the volume of the entire solid, we then add the volumes of all the shells and obtain. Question Find the volume of the solid generated by revolving the following region about the given axis. There are 2 steps to solve this one. If the cylindrical shell has a radius r and height h, then its area will be 2rh. Answered Find the volume of the solid generated bartleby. How do you find the volume of the solid generated by revolving the region bounded by the graphs y2x2, y0, x2, about the x-axis, y-axis, the line y8, the line x2 Calculus Applications of Definite Integrals Determining the Volume of a Solid of Revolution. Question Find the volume of the solid generated by revolving the region inside the circle x2 y2 -9 and to the right of the line x 2 about the y- axis. Please make the solution and steps easy to follow. For y-axis input x0 and for x-axis input y0. The volume of this representative shell is 2pirh " thickness" The radius is. Use the disk method to find the volume of the solid of revolution generated by rotating the region between the graph of f (x) 4x f (x) 4 x and the x-axis x -axis over the interval 0,4 0, 4 around the x-axis. where, r 1 2 (r1 r2) r1 radius of right end r2 radius of left end r 1 2 (r 1 r 2) r 1 radius of right end r 2 radius of left end. Find the volume of the solid of revolution generated when the finite region R that lies between y 4 x 2 and y x 2 is revolved about the x -axis. Thus the volume by shell method is 2rh times its thickness. Find the volume of the solid generated by revolving the region bounded by y 3, x 3 and x 3y2 about the x-axis. First graph the region R and the associated solid of revolution, as shown in Figure 6. The first thing to understand is where the curves intersect. Example 1 Finding the Volume of the Solid Generated by the Revolution of the Region Bounded by a Given Line around the -Axis. (Round your answer to three decimal places. Find the volume of the solid of revolution generated when the finite region R that lies between y 4 x 2 and y x 2 is revolved about the x -axis. May 19, 2018 How do I find the volume of the solid generated by revolving the region bounded by yx2, y0, and x2 about the x-axis The y-axis Calculus Applications of Definite Integrals Determining the Volume of a Solid of Revolution. How do you find the volume of the solid generated by revolving the region bounded by the graph. If the cylindrical shell has a radius r and height h, then its area will be 2rh. So our functions will need to be functions of x Revolving about the y axis will result in a cylindrical shell. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. Step 1. Answer Since were revolving about the x-axis, we need to integrate with respect to y (using the shell method). Our online calculator, based on Wolfram Alpha system is able to find the volume of solid of revolution, given almost any function. Jul 23, 2017 See the answer below. There are three ways to find this volume. This problem has been solved You&39;ll get a detailed solution from a subject matter expert that helps you learn core concepts. Problem 40E Find the exact volume of the solid that results when the region bounded in quadrant I by the axes. 5 X Need Help Watch It Read It Talk to a Tutor Save Progress Submit Answer Find the volume of the solid generated by revolving the specified region about the given line. First we need to determine the bounds We can do this by setting both equations equal to each other 9-x29-3x 0x2-3x 0x(x-3) x0,3 Now we can apply the washer method V . Publisher Cengage,. Jun 8, 2015 First, try and imagine how it would look. 5- The volume of the solid generated by revolving the shaded region about the y-axis is (Type an exact answer, using T as needed. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Find the volume of the solid generated by revolving the region bounded by the graphs of yx25 and yx7 about the x-axis The volume of the solid is cubic units. ) cubic units. Publisher PEARSON. Jun 28, 2017 The objective is to find the volume of the solid generated by revolving the curve y&92;&92;dfraca3a2x2 about its asymptote. The volume is given by. the washer method a. In general, suppose y f(x) is nonnegative and continuous on a, b. ) YA 4 8 y2x R y 8 yx. For purposes of this discussion let&x27;s rotate the curve about the x x -axis, although it could be any vertical or horizontal axis. Find the volume of the solid generated by revolving the region R bounded by y e X, y0, x 0 and x In 3 about the x-axis. ) Sketch the region bounded by the curves y2x and y2x3 then find the volume of the solid generated by. (c) Find the volume of the solid generated by revolving R about the y -axis. To calculate the volume of a cylinder, then, we simply multiply the area of the cross-section by the height of the cylinder V A h. Aug 6, 2019 The following problem is from the book, Calculus and Analytical Geometer by Thomas and Finney. Question Given the region bounded by the graphs of y ln x, y 0, and x e, find the following. Use the shell method to find the volume of the solid generated by revolving the regions bounded by the curves and lines 7. Heres the best way to solve it. Find the volumes of the solids generated by revolving the region between y 4x and y about a) the x-axis and b) the y-axis. ) b. Use the shell method to find the volume of the solid generated by revolving the region bounded by the line y 6x 7 and the parabola yx2 about the following lines. We see that a cross section of this solid is a washer with area A(y) (outer radius)2 (inner radius) 2 (p. In the following parts, let R be the region bounded by the curves y2x3,y0, and x1. (c) Find the volume of the solid generated by revolving the region about the y-axis. The region bounded by the graphs of &92;(yx, y2x,&92;) and the &92;(x&92;)-axis. Use the method of cylindrical shells to find the volume of the solid generated by revolving the area enclosed by y - x 3 2 x 2 - x 2 and y -x 1 in the first quadrant. Here is a picture of the region and a representative slice taken parallel to the axis of rotation. Question Given the region bounded by the graphs of y ln x, y 0, and x e, find the following. To see this, consider the solid of revolution generated by revolving the region between the graph of the function &92;(f(x)(x1)21&92;) and the &92;(x&92;) -axis over the interval &92;(1,3&92;) around the. Find the surface area of the solid generated by revolving the arc of the parabola y 2 4 a x. I am having a little trouble figuring out how to integrate this problem. We see that a cross section of this solid is a washer with area A(y) (outer radius)2 (inner radius) 2 (p. show all steps please thanks sketch the region bounded by the curves y5x, y0, and x2. Show Solution. 19 Find the volume of the solid generated by revolving the shaded region about the y-axis. From the graphs of these expressions in can be seen that ysqrt x3 has a greater area than y x2 so we must find the area under y x2 and subtract it from the area under ysqrt x3 and then revolve this area about the x axis between the bounds x1, x 0 Volume of revolution is given by piinta. In the preceding section, we used definite integrals to find the area between two curves. (10 points) Let R be the region bounded by the curve yx26x9 and the line y6. Sketch the region bounded by the curves y2x3,y2 and x0 then find the. an area around a different axis than the axis the area touches). Final answer. approx 152. Nov 16, 2022 Example 1 Determine the volume of the solid obtained by rotating the region bounded by &92;(y x2 - 4x 5&92;), &92;(x 1&92;), &92;(x 4&92;), and the &92;(x&92;)-axis about the &92;(x&92;)-axis. The line x10 c. where, r 1 2 (r1 r2) r1 radius of right end r2 radius of left end r 1 2 (r 1 r 2) r 1 radius of right end r 2 radius of left end. This problem has been solved You&39;ll get a detailed solution from a subject matter expert that helps you learn core concepts. Sketch the region bounded by the curves y 8x, y 0 and x 2 then find the volume of the solid generated by revolving this region about the x-axis. Question Sketch the region bounded by the curves y2x3,y2 and x0 then find the volume of the solid generated by revolving this region about the x-axis. Free volume of solid of revolution calculator - find volume of solid of revolution step-by-step. The area of each slice is the area of a circle with radius f (x) f (x) and A r2 A r 2. Find the volume of the solid generated by revolving the shaded region about the The volume of the solid is cubic units x-axis (Type an exact answer using x as needed) 5x4y20 Incorrect Find the volume of the solid generated by revolving the shaded region about the y axis The volume of the solid generated by revolving the shaded region about the y axis is (Type an exact answer, using x as needed). If the volume is not defined, enter DNE. Example 1 Volumes of Solids of Revolution. where, r 1 2 (r1 r2) r1 radius of right end r2 radius of left end r 1 2 (r 1 r 2) r 1 radius of right end r 2 radius of left end. In part (b) students had to calculate the volume of the solid generated by rotating the region about the horizontal line y 3, a line that. Example 6. Find the volume of the solid of revolution generated when the finite region R that lies between (y 4 x2) and (y x 2) is revolved about the (x)-axis. V is the volume of the three-dimensional object, A is the area of the two-dimensional figure being revolved, and d is the distance traveled by the centroid of the. Hot Network Questions. Ans. Using the shell method, set up the integral to find the volume of the solid generated by rotating the region bounded by yx and y 6x about the x. ) Sketch the region bounded by the curves y2x and y2x3 then find the volume of the solid generated by. How do you find the volume of the solid generated by revolving the region bounded by the graph. The volume of the solid generated by revolving the region bounded. Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x-axis. only fans keaks, liger movie download filmyzilla 480p filmyzilla
yx3 y 0 x 3 (a) the x-axis (b) the y-axis (c) the line x 6. . Find the volume of the solid generated by revolving
Please make the solution and steps easy to follow. Volume of a Solid of Revolution Disk Method If the region bounded by the curve y f (x), the x -axis, x a, and x b is revolved about the x -axis, the volume of the solid generated this way is V a b f (x) 2 d x. The volume is. y 81 x 2 , y 0 The volume of the solid is. This is shown as the shaded area. c2 (x 2c sinh(2xc)) (b) Determine the volume of solid generated by revolving the plane area bounded by y 2 4x and x 4 about the line x 4. Solution to Example 2 The graphs of y - x 3 2 x 2 - x 2 and y -x 1 are shown below. y y 0 X 1 Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the x-axis. Calculus questions and answers. Use symbolic notation and fractions where needed. The line y 11 f. View Solution. Use the Shell Method (SET UP ONLY) to find the Volume of the Solid formed by revolving this region about a. Find the volume of the solid generated by revolving the region bounded by x 4y 4 and the yaxis in the interval -3, 3. Select the correct answer below method of cylindrical shells disk method. I'm having. O obb 10- 8- 6 4 2 0- 0 1 2 3 4 5 ON cubic units. Question Use the shell method to find the volume of the solid generated by revolving the region bound by y3x,y0, and x3 about the following lines. V 4R 1 2r2 22r2R. yx, y2x, y8 The volume of the solid is cubic units. The slice is taken at some value of x and has thickness dx. y 9 x2 y0 x 2 x 3. 6) The region enclosed by x y13 x 0, y 27 Find the length of the curve. This could be described as a "cone" where the tracing of the surface starting from every point on the base&39;s circumference (at the same time) grows like x2 until you reach the tip. (Type an exact answer in terms of pi. (a) Find the area of R. we can already see that (dA)dx dx to 0 pi (2 (1x. The line x 10 c. V a b 2 r h d x b a 2 x f (x) d x. find the following. In the following parts, let R be the region bounded by the curves y 2x3,y 0, and x 1. the shell method b. The "red volume" can be found by the cylindrical shell method. The line y11 f. Find the volume of the solid of revolution formed by revolving R R around the y-axis. Shell method is a contrast method to the discwasher method to find the volume of a solid. Sorted by 1. volume of the solid formed by revolving the region bound by yx and yx2 about the y axis. If the region bounded. y 0. V 4R 1 2r2 22r2R. 33n 40 b) 7 54 61x 68. 5 X Need Help Watch It Read It Talk to a Tutor Save Progress Submit. I got the answer using the diskwasher method, but I wanted to try solving using the cylindrical method as well. When we use the slicing method with solids of revolution, it is often called the disk method because, for solids of revolution, the slices used to over approximate the volume of the solid are disks. The volume is 107. In general, suppose y f(x) is nonnegative and continuous on a, b. About the y-axis 20. (c) Find the volume of the solid generated by revolving R about the y-axis. 0 Volume of the solid generated by revolving the region R enclosed by the curve - Disk and Shell method. Calculus questions and answers. ) YA 4 8 y2x R y 8 yx. The objective is to find the volume of the solid generated by revolving the curve y a3. The y-axis b. How to find the volume of a solid of revolution generated by revolving a region bounded by the graph of a function around one of the axes using definite integrals We will. O obb 10- 8- 6 4 2 0- 0 1 2 3 4 5 ON cubic units. Volume of Rotation Between Two Solids. When we use the slicing method with solids of revolution, it is often called the disk method because, for solids of revolution, the slices used to over approximate the volume of the solid are disks. Find the volume of the solid generated by revolving the region bounded by y 3x, y0, and x 3 about the x-axis. Use the shell or washer method. There are 2 steps to solve this one. the centroid of an half is located at (xC, 0) with. About the x-axis 18. The blue plus red volumes should sum to the volume V 32 3. xC 1 2 4 4 2 3r cos r2d a22 2 3a 4 4 cos cos3 2 (2)d 2 3a 3 8 2 2 8 a. 86cubic units Refer to the figure below The generator region is Region A limited by yx(12), y2 and x0 (the y-axis). Find the volumes of the solids generated by revolving the region between y 5 Squareroot x and y x22 about a) the x-axis and b) the y-axis. 2 Answers. Question Given the region bounded by the graphs of y ln x, y 0, and x e, find the following. To find the volume of the solid, first define the area of each slice then integrate across the range. Example Find the volume of the solid generated by revolving the region bounded by x p 1 y2 and the line x 12 about the yaxis. y ex, y 0, x 0 (a) Find the area of the region. Find the volume of the solid of revolution generated when the area described is rotated about the x-axis. (Give answer. yx, y2x, y8 The volume of the solid is cubic units. Volume of a Solid of Revolution Disk Method If the region bounded by the curve y f (x), the x -axis, x a, and x b is revolved about the x -axis, the volume of the solid generated this way is V a b f (x) 2 d x. Setting up the definite integral for the volume of a solid of revolution around a vertical line using the "washer" or "ring" method. 12pi2 4. 1)Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines. Finding volume of a solid of revolution using a washer method. Find the volume of the solid generated by revolving the region bounded by y 3 Squareroot sin x, y 0, and x1 pi3 and x2 pi3 about the x-axis. Next, use the disc method to find the volume (y r). y 9 x2 y0 x 2 x 3. For a function rotated about the x-axis, the volume is given by. The volume of the resulting solid is (Type an exact answer. y cos x2, y sin x2, x 0, x 2. ) volume Find the volume of a solid of revolution generated by revolving this region about the y-axis. Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y ex and the line x ln 8 about the line x ln 8. 4. The line y -1 b. Finding volume of a solid of revolution using a shell method. The volume of the solid generated by rotating the region bounded by f (x) x2 4x 5, , and the x-axis about the x-axis is 5 78S units cubed. Select the best method to find the volume of a solid of revolution generated by revolving the given region around the &92;(x&92;)-axis, and set up the integral to find the volume (do not evaluate the integral) the region bounded by the graphs of &92;(y2x2&92;) and &92;(yx2&92;). (b) Find the volume of the solid generated by revolving the region about the x-axis. Sketch the region bounded by the curves y8x,xy9 and y2 then find the volume of the solid generated by revolving this region about the x-axis. (Give answer in exact form. Answered Find the volume of the solid generated bartleby. ) There are 2 steps to solve this one. Parametric representations of surfaces. I am having a little trouble figuring out how to integrate this problem. Here, an elementary area , in the form of a rectangle of length f(x) and width triangle x, is revolved about its base on the x-axis, to generate an elementary solid of revolution that is in the form of a circular disc of radius f(x) and thickness triangle x. Calculus questions and answers. color(blue)(pi3 "cubic units. ) 1612 5 b. (answer in terms of pi) There are 3 steps to solve this one. The region in the first quadrant bounded above by the curve yx, below by the x-axis, and on the right by the line x 1, about the line x - 3. Oct 22, 2015 So if I have to find the volume of the solid generated by revolving the region bounded by x0, yx2, and y-x2 around the y-axis, I would use shells because there would only be one integral to evaluate. The region bounded by the graphs of &92;(yx, y2x,&92;) and the &92;(x&92;)-axis. Find the volume of the solid generated by revolving the region bounded by the parabola y - 16 and the line y -1 about the following lines. I am having a little trouble figuring out how to integrate this problem. The region in the first quadrant bounded above by the line y 2 3, below by the curve y cscxcotx, and on the right by the line x 2, about the line y 2 3. 23408 views around the world You can reuse this answer Creative Commons License. (Type an exact answer, using as needed. Compute answers using Wolfram&39;s breakthrough technology & knowledgebase, relied on by millions of students & professionals. . craigslist texoma farm and garden