Integrating x * (cos x)^ n between pi/2 and 0

[ZakS]

Would anyone be able to help me do this? I have tried by parts, but did not make progress. As n gets large, the area gets smaller.

Your help is appreciated.

Z

 

[ehild]

You might apply that cos(x)=(e^ix+e^-ix)/2

ehild

 

[Bohrok]

Try integration by parts just once and use the formula for ∫cosⁿx dx twice.