Question

Diverges or converges?

Answer 1

\[\LARGE \int_{0}^{\infty}~sin^2 \alpha~d \alpha\]
I'm assuming diverges but I'm not sure how to show it.

Answer 2

\[\large \int \limits_0^{\infty} \sin^2 \alpha d\alpha = \lim \limits_{t\to \infty }\int \limits_0^{t} \sin^2 \alpha d\alpha \]

Answer 3

evaluate the integral and take the limit

Answer 4

right

Answer 5

use this :

\(\sin^2 x = \dfrac{1-\cos (2x)}{2}\)