# Volume of Revolution Problem

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Find the volume of the solid of revolution formed by rotating the finite region bounded by the graphs of y=sin((pi)x^2)/2) and y=x^5 about the y-axis.

The possible answers are:

A. 2(5pi-7)/7 B. (7pi-5)/7 C. 2(5-pi)/7

D. (5pi+2)/7 E. 2(7-pi)/7

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4. Find the volume of the solid of revolution formed by rotating the finite region bounded by the graphs of y=sin((pi)x^2)/2) and y=x^5 about the y-axis.

I believe I am supposed to use this equation for the volume:

Vshell = 2pi*rhdx

And set it up like this:

2pi*x*(sin((pi)x^2)/2) - x^5)dx

The equation is correct.

The two curves intersect at x = 0 and x = 1.

So the volume is

A. 2(5p-7)/7 B. (7p-5)/7 C. 2(5-p)/7

D. (5p+2)/7 E. 2(7-p)/7

So E is the correct answer.

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