help-computing definate integrals?

Question

Answer 1

(1)

Step 1:

The integral is .

Sum and difference rule of integral : .

Power rule of integral formula : .

                            

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Solution :

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Answer 2

(2)

Step 1:

The integral is .

Sum and difference rule of integral : .

Power rule of integral formula : .

                            

.

Solution :

.

Answer 3

(3)

Step 1:

The integral is .

Domain :

All possible values of z is the domain of the function.

The domain of the function is .

Therefore the function is not continuous at .

Improper integrals :

If f  is discontinuity at c, where , and both and are convergent.

Then .

Therefore the integral is .

Step 2:

Consider .

Sum and difference rule of integral : .

Power rule of integral formula : .

                            

.

Comments

Step 3:

Consider .

Sum and difference rule of integral : .

Power rule of integral formula : .

                             

.

Solution :

.