Evaluate the following Integrals:

Let

We have sin 2x = 2 sin x cos x

Put sin x = t

⇒ cos x dx = dt (Differentiating both sides)

When x = 0, t = sin 0 = 0

So, the new limits are 0 and 1.

Substituting this in the original integral,

We will use integration by parts.

Recall

Here, take f(t) = tan^-1t and g(t) = t

Now,

Substituting these values, we evaluate the integral.

We can write

Recall