Prove that - -0a x2a - xn dx - 2an - 3n - 1n - 2n - 3

∫ _ 0 ^ a x ^ 2 ( a x ) #160; ^ n dx=[ x ^ 2 ( a x ) #160; ^ n+1 n+1 +( 2x( a x ) #160; ^ n+2 ) #160; n+2 + 2x( a x ) #160; ^ n+3 n+3 ...

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Coordinate Geometry

Prove that : ...

Question

Prove that :
$\int_{0}^{a} x^{2} (a - x)^{n} d x = \frac{2 a^{n + 3}}{(n + 1) (n + 2) (n + 3)}$

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