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. 
].