Question

Question #17bd1

Answer 1

See.the explanation, for proof.

Explanation:

Let I be the definite integral and `x =pi-t`. The limits become `pi`

and 0, and dx = `-dt`. .

Now, `I=-int(pi-t)f(sin(pi-t)) dt`, from `t= pi` to t = 0.

`=pi int f(sin t) dt-int t f(sin t) dt`, from t = 0 to `pi`,

using `sin (pi-t)=sin t`,

`=pi int f(sin x) dx`, from x = o to x =`pi -I`.

Thus,`I = pi/2 int f(sin x) dx`, from x = 0 to x =`pi`.