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(c) Use the cylindrical shells method to find the volume of the solid generated when the region enclosed by the curves y = x³, y = 1, and x = 0 is revolved about the line y = 1.

(c) Use the cylindrical shells method to find the volume of the solid generated when the region enclosed by the curves y = x³, y = 1, and x = 0 is revolved about the line y = 1.

Advanced Engineering Mathematics
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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answer part c

(a) Let R be the region enclosed by the curves y=x²+2 and y=x+4. (i) Sketch the region R. (ii) Find the area of the region R. (b) Consider the region enclosed by the curves y = cos x, y = sin x and the lines x== 41 Compute the volume of the solid of revolution obtained by revolving the region about the x- axis using disk/washer method. (c) Use the cylindrical shells method to find the volume of the solid generated when the region enclosed by the curves y=x²³,y=1, and x = 0 is revolved about the line y=1. (d) The curve y=√16-x²,-3≤x≤3 is an are of the circle x² + y² = 16. Find the area of the surface obtained by rotating this are about the x-axis.
Transcribed Image Text:(a) Let R be the region enclosed by the curves y=x²+2 and y=x+4. (i) Sketch the region R. (ii) Find the area of the region R. (b) Consider the region enclosed by the curves y = cos x, y = sin x and the lines x== 41 Compute the volume of the solid of revolution obtained by revolving the region about the x- axis using disk/washer method. (c) Use the cylindrical shells method to find the volume of the solid generated when the region enclosed by the curves y=x²³,y=1, and x = 0 is revolved about the line y=1. (d) The curve y=√16-x²,-3≤x≤3 is an are of the circle x² + y² = 16. Find the area of the surface obtained by rotating this are about the x-axis.
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