(a)

The integral is .

The radicand is .

Completing the square of the radicand.

Thus, the integral is .

Let , then .

Substitute corresponding values in .

Apply formula :  .

Substitute in above expression.

Thus, .

(b)

The integral is .

Let , then .

Substitute corresponding values in .

Apply formula :  .

Substitute in above expression.

Thus, .

(c)

Domain of is .

Domain of antiderivative obtained in part (a) is , i.e, .

Domain of antiderivative obtained in part (b) is , i.e, .

The antiderivative obtained in part (a) is .

The antiderivative obtained in part (b) is .

Draw a coordinate palne.

Graph the functions and in the domain .

Graph :

.

Observe the above graph : The antiderivative obtained in part (a) and (b) appear to be significantly different.

(a)

.

(b)

.

(c)

Graph :

.

Domain of antiderivative obtained in part (a) is , i.e, .

Domain of antiderivative obtained in part (b) is , i.e, .