The value of ∫0π sinn⁡xcos2m+1⁡xdx is

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.