The integral is .

(a)

Find the integral using trignometric substitution.

Let .

Differentiate on each side.

.

Consider .

Substiute the corresponding values.

From the figure .

Now apply the limits.

(b).

The limits obtained by the trignometric substitution are

If , then .

If , then .

When .

.

(a).

By the integration limits :

.

(b).

By the limits obtained by the trignometric substitution:

.