(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Rotate around the y-axis the region above the graph of y=x^{3}that is bounded by the lines x=1 and y=8

2. Relevant equations

dV= (2pix)(y)(dx)

3. The attempt at a solution

dV = (2pix)(y)dx

dV = (2pix)(x^3) dx

= 2pix^4

I integrated from y = 1 to y=8 and I get the wrong answer.

V = 2∏_{x=1}∫^{x=2}x^4 dx

V = 2∏[1/5x^5]^{2}_{1}

Can someone please explain to me, how I would set up this equation? Something to do with the first function subtracting the second function which I think is x=1

Here is a graph: http://www3.wolframalpha.com/Calculate/MSP/MSP15491a07c8557bi4590b00001ibd52eb6gcc3177?MSPStoreType=image/gif&s=21&w=366&h=298&cdf=RangeControl [Broken]

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# Homework Help: Volume by Cylindrical shells

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