help-[computing definate integrals]?

Question

Answer 1

5)

Step 1:

The integral is .

Rewrite the integral.

Sum property of Integrals :.

 

.

Solution:

.

Answer 2

4)

Step 1:

The integral is .

Definition of improper integral :

If  has a discontinuity at  , where , and both  and  are convergent, then

.

Here the third term in the integrand function  has a discontinuity at ,

.

Consider .

Sum property of integrals :.

.

.

Step 2:

Consider .

.

.

.

.

Solution:

.

Answer 3

6)

Step 1:

The integral is .

Sum property of Integrals :.

Rewrite the integral as

.

Solution:

.