Integration Question #2

I came across the integral a few days ago. Pretty interesting, many ways to solve this integral, be it graphically or by substitution.

\int_a^b \sqrt{(x-a)(b-x)} dx =?

Answer: \pi \frac{(a-b)^2}{4}

Hint: Consider the graph of y = \sqrt{(x-a)(b-x)}, it should give a semicircle which centre is (\frac{a+b}{2},0)

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