The value of ∫$$0$$π sinn⁡$$xcos2m+1$$⁡xdx is

Correct option is 3∫0π cos2m−1⁡xdx

Questions

The value of $\int_{0}^{π} \sin^{n} x \cos^{2 m + 1} x d x$ is

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(2m+1)!(n!)2

(2m+1)!n!

∫0π cos2m−1⁡xdx

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detailed solution

Correct option is C

I=∫0π sinn⁡xcos2m+1⁡xdx =∫0π sinn⁡(π−x)cos⁡2m+1(π−x)dx =−∫0π sinn⁡xcos⁡2m+1xdx=−ISo 2I=0 which implies that I=0 Also, ∫0π cos2m−1⁡xdx=0by a similar reasoning.

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The value of ∫0π sinn⁡xcos2m+1⁡xdx is

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The value of $\int_{0}^{π} \sin^{n} x \cos^{2 m + 1} x d x$ is