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$$\int_{a}^{b} \frac{\sqrt{(r-a)(b-r)}}{r}dr$$ where a and b are constant lower and upper limit. The answer of this integral is $$\pi/2({a}^{1/2}-{b}^ {1/2})^{2}$$ so please give me the hints that how to solve this integral thanks in advanced sir.

garserdt216
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umairkhan
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    The problem in an equivalent form was solved 3 years later. https://math.stackexchange.com/questions/3343625 – Y.D.X. Jun 15 '24 at 14:39

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hint: If you let $f(x) = \sqrt{(x-a)(b-x)}$, then $f(x) = f(a+b-x)$. How do you use this property to get to the finish line ?

DeepSea
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  • Thank you. Your hint would be useful, except I have tried now for a day and I've yet to see how to use it properly. Can I have maybe a partial answer? This isn't my homework. – umairkhan May 20 '17 at 14:49