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

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

y = 5x, y = 5[itex]\sqrt{x}[/itex] about y = 5

2. Relevant equations

A(x)=∏(R^{2}-r^{2})

3. The attempt at a solution

A(x)=∏(5x)^{2}-(5[itex]\sqrt{x}[/itex])^{2})

A(x)=∏(25 x^{2}- [itex]\frac{10}{3}[/itex]x^{[itex]\frac{3}{2}[/itex]})

V=∏[itex]\int[/itex][itex]^{1}_{0}[/itex](25x^{2}- [itex]\frac{10}{3}[/itex]x^{[itex]\frac{3}{2}[/itex]})dx

V=∏([itex]\frac{25}{3}[/itex]x^{3}-[itex]\frac{4}{3}[/itex]x^{[itex]\frac{5}{2}[/itex]}) {0,1}

V=∏([itex]\frac{25}{3}[/itex]-[itex]\frac{4}{3}[/itex])

V= [itex]\frac{21}{3}[/itex]∏

Where did I go wrong? I can't figure out the about y=5. If I am correct, you would usually subtract 5 from the two radii, but since they intersect at y=5, the just flip on that intersection point and thus we don't need to find the lost area. Bad explanation, I know, maybe someone can explain it to me.

Thanks in advance!

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# Homework Help: Find the volume of the solid obtained by rotating the region

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