# Mathematical problems for self assessment

###### Sample Problems

**INTEGRATION I**

1. Evaluate the indefinite integrals:

(i)

(ii)

[Ans. (i) (ii) ]

2. Evaluate the indefinite integrals:

(i)

(ii)

[Ans. (i) (ii) ]

3. Calculate the area under the curve between *x* = 1 and *x* = 2.

[Ans. 15/4]

4. Calculate the area bounded by the curves and over the region .

[Ans. 3π ]

5. Evaluate the definite integrals:

(i)

(ii) (Hint: Use integration by parts)

[Ans. (i) (ii) ]

6. Using integration by parts evaluate the indefinite integral

[Ans. ]

7. Using integration by parts evaluate the definite integral

[Ans. ]

8. Evaluate the improper integral

[Ans. ]

9. Using integration by parts find a reduction formula for the improper integral

and hence evaluate

[Ans. ].