Question
Asked Sep 16, 2019
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Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.

y = 3sqrt(x); y = 0; x = 0     Rotating around x = -3;
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Expert Answer

Step 1

Find the volume of the solid obtained by rotating region as follows.

The solid bounded by the region y=3dx, y = 0 and x= 0 about the line
x=-3
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The solid bounded by the region y=3dx, y = 0 and x= 0 about the line x=-3

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Step 2

Use online graphing calculator to draw the functions as follows.

(0,0)
Here, the area of the region is a point.
Thus, the limit points of x 0 to 0. That is, a single point
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(0,0) Here, the area of the region is a point. Thus, the limit points of x 0 to 0. That is, a single point

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Step 3

Find the area of the re...

Surface area of cylindrical shell =27rh
2T(x-(-3)) (3-)
=27(x+3) (3x)
= 27t( 3XVX +9Vx
3
1
=27 3x2 9x2
help_outline

Image Transcriptionclose

Surface area of cylindrical shell =27rh 2T(x-(-3)) (3-) =27(x+3) (3x) = 27t( 3XVX +9Vx 3 1 =27 3x2 9x2

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Calculus

Integration

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