Question

Evaluate the integral.

Answer 1

Try substitution: u = sin(x), or maybe u = (sin(x))^2

Answer 2

let sinx =t
on differentiating both sides
we get
cosxdx=dt
putting this in the equation our integral becomes\[\int\limits_{0}^{\pi} t ^{2}dt\]
integrating we get
\[t^{3}/3\] with limits 0 to pi
now putting the value of t=sinx
we can solve the limits to get answer zero

Answer 3

Or, we could just observe that the period of the function in the argument is \(\pi\) and just observe that the integral is zero.

Answer 4

Just do a u-substitution for sin(x) and integrate. From here it should be straight forward.