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We can write this as $\displaystyle 2\pi |a|\int_0^b \sqrt{x}\sqrt{1+ \frac{a^2}{4x}}dx$. That is the same as $\displaystyle 2\pi a \int_0^b \sqrt{x+ \frac{a^2}{4}}dx$. Can you integrate that?
Last edited by HallsofIvy; Jul 8th 2018 at 12:32 PM.