help?[substitution definite integral]??

Question

Answer 1

(1)

Step 1:

 The integral is .

Let .

Apply derivative on each sid with respect to .

.

Step 2:

Substitute and in integral.

Substitute .

.

.

Solution:

.

Answer 2

(2)

Step 1:

The integral is .

Let

Apply derivative on each side with respect to .

.

Substitute and in the integral.

Again using substitution method.

Let .

Apply derivative on each side with respect to .

.

Step 2:

Substitute and in .

Comments

Contd...

Substitute .

Substitute .

.

.

Solution:

.

Answer 3

(3)

Step 1:

The integral is .

Sum property of Integral :.

Find the value of .

.

Step 2:

Find the value of .

Apply derivative on each side with respect to .

Substitute  and  in .

Integration of exponential function :.

.

Comments

Contd..

Step 3:

.

Solution:

.

Answer 4

4)

Step 1:

The integral is .

 

Evaluation of the integral is not possible.

Continuity Implies Integrability Theorem:

If a function is continuous on the closed interval , then is integrable on .

The function is not continuous at on .

The second term in the integral cannot be integrated on .

If even one term in the integral cannot be integrated then the whole integral cannot be done.

Solution:

Evaluation of the integral is not possible.