(3) \ \

Step 1: \ \

The integral is . \ \

\ \

. \ \

Step 2: \ \

\ \

\ \

Substitute and in .

\ \

Step 3: \ \

\ \

Solution: \ \

.

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. \ \