Question

How to evaluate the definite integral (0,1) ∫ cos(πt/2)dt ?

Answer 1

Refer to explanation

Explanation:

Set `u=pi*t/2=>du=pi/2dt` and integration limits are

`t=1=>u=pi/2` and `t=0=>u=0` hence the integral becomes

`int_0^(pi/2) (2/pi)*cosudu=(2/pi)*[sin]_0^(pi/2)=2/pi`