The integral is .

(a)

Find the integral using trigonometric substitution. 

Let .

Differentiate on each side.

.

Consider .

Substitute the corresponding values.

From the figure .

Apply the limits.

(b).

The limits obtained by the trigonometric substitution are

If , then .

If , then .

When .

.

(a).

By the integration limits :

.

(b).

By the limits obtained by the trigonometric substitution:

.