definite integral (1 Viewer)

[juantheron]

where

 

[seanieg89]

Let f(x) be your integrand and let I be the sought definite integral.

It is easy to show f(x)+f(pi/2-x)=1.

Integrate this expression between the given limits and make the substitution u=pi/2-x to arrive at I=pi.

(Note that the integral of a T-periodic function over any interval of length T is the same.)

 

[juantheron]

thanks seanieg89