In Exercises 23-26, use the shell method to find the volumessolids generated by revolving the regions bounded by the givenabout the given lines.24. y = x', y = 8, x = 0a. The y-axis264b. The line x = 3c. The linex =-2d. The x-axis336936e. The line y = 88 S76f. The line y = -1%3D

Given the curves as y=x3, y=8 ,x=0 solving for the intersection point ⇒x3=8⇒x3-8=x-2x2+2x+4…

Answered: In Exercises 23-26, use the shell…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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In Exercises 31–32, find the volumes of the solids generated by revolving the regions about the given axes. If you think it would be better to use washers in any given instance, feel free to do so. 31. The triangle with vertices (1, 1), (1, 2), and (2, 2) about a. the x-axis b. the y-axis c. the line x = 10/3 d. the line y = 1 32. The region bounded by y = srqt(x), y = 2, x = 0 about a. the x-axis b. the y-axis c. the line x = 4 d. the line y = 2
A region is bounded in the plane by the lines: y=-x+3, y=2x-6, and y=3. Find the volume of the solid given by rotating around the line x=5 using the shell method.
A solid is formed by revolving about the y-axis, the area bounded by the curve x³=y, the y-axis and the line y=8. Find its centroid .
In Exercises 1–12, use the method of shells to find the volume of the solid obtained by revolving the region bounded by the given curves about the y-axis. 1. y = x2, y2 = 8x 2. y = x2 - 2x, x-axis
find the center of mass of a thin plate of constant density d covering the given region. 1. The region bounded by the parabola y = x2 and the line y = 4 2. The region bounded by the parabola y = 25 - x2 and the x-axis.
Find the valume of the solid generated by revolving the region bounded by y= -2x2 and y= x2 - 3, in the 4th quadrant about the : the line x =-1 the line y =4
Find the volume of the solid generated by revolving the region bounded by the graphs ofthe equations about the given lines.y=√x, y=0, x=3 the line ? = 6.
Below are two perspectives of the surface bounded solid x2 + z2 = 4 and x2 + y2 + z2 = 16, in the first octant. the two perspectives of the solid are in the first attached image. An expression that allows calculating the volume of the solid corresponds to: the answers are in the second attached image.
FIND THE VOLUME OF THE SOLID FORMED BY REVOLVING THE GIVEN AREABOUNDED BY THE LINES AND CURVES, ABOUT A GIVEN AXIS OF ROTATION. 2. The area bounded by y=3x+4 and the curve y=x² is revolved about the line x =5.
Consider a thin plate of constant density d lying in the regionbounded by the graphs of y = √x and x = 2y. Find the plate’s mass.
Consider a thin plate of constant density d lying in the regionbounded by the graphs of y = √x and x = 2y. Find the plate’s center of mass.
For some regions, both the washer and shell methods work well for the solid generated by revolving the region about the coordinate axes, but this is not always the case. When a region is revolved about the y-axis, for example, and washers are used, we must integrate with respect to y. It may not be possible, however, to express the integrand in terms of y. Compute the volume of the solid generated by revolving the triangular region bounded by the lines 2y = x + 4, y = x, and x = 0 about the x-axis using the washer method.

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In Exercises 23-26, use the shell method to find the volumes solids generated by revolving the regions bounded by the given about the given lines. 24. y = x', y = 8, x= 0 264 a. The y-axis b. The line x = 3 %3D c. The line x = -2 d. The x-axis 336r 936 e. The line y = 8 f. The line y = -1 576 %3D