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

Evaluate the definite integral for the area of the surface generated by revolving the curve about the x-axis.

y=(x^{3}/6) + (1/2x), [1,2]

2. Relevant equations

2π∫[r(x)](1+[f'(x)^{2}])

3. The attempt at a solution

First I found the derivative.

f'(x)= (x^{2}/2) + (1/2x^{2})dx

And since y is a function of x, r(x) is

r(x)= (x^{3}/6) + (1/2x)

Then I plug everything in and get

2π∫ [(x^{3}/6) + (1/2x)] * {1 + [(x^{2}/2) + (1/2x^{2})]^{2}}^{1/2}}dx

And then I'm stuck. The book tells me that I am suppose to get

2π∫ [(x^{3}/6) + (1/2x)] * [(x^{2}/2) + (1/2x^{2})]dx

But I have no idea how they got that. Specifically, I don't know how they got rid of the radical...

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# Homework Help: Evaluate the definite integral for the area of the surface.

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