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  4. The value of ∫ limitsπ0 sin50 x cos49 x dx is

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Q. The value of $\int\limits^{\pi}_{0} \sin^{50} \,x \,\cos^{49} x\, dx$ is

WBJEEWBJEE 2011Integrals

Solution:

Let $ I =\int\limits_{0}^{\pi} \sin ^{50} x \cos ^{49} x d x $
$=\int\limits_{0}^{\pi} \sin ^{50}(\pi-x) \cos ^{49}(\pi-x) d x $
$=-\int\limits_{0}^{\pi} \sin ^{50} x \cos ^{49} x d x $
$ \Rightarrow I =-I \Rightarrow I=0 $