Mathematics for Biomedical Engineering
Sample Problems
INTEGRATION II
1. By making an appropriate substitution in each case evaluate the integrals:
(i) 
(ii) 
(iii) 
[Ans. (i) 
(ii) 
(iii) 
]
2. By making the substitution 
evaluate the indefinite integral
[Ans.
]
3. By making the substitution 
evaluate the indefinite integral
[Ans.
or 
]
4. By completing the square evaluate the following integrals
(i) 
(ii) 
[Ans. (i) 
(ii) Ans. 
]
5. Evaluate the indefinite integrals:
(i) 
(ii) 
[Ans. (i) 
(ii) 
]
6. Evaluate the integrals:
(i) 
(ii) 
(iii) 
[Ans.(i) 
(ii) 
(iii) 
]
7. Using partial fractions evaluate the definite integrals:
(i) 
(ii) 
[Ans.(i) 
(ii) 
]
8. Using partial fractions evaluate the indefinite integral
[Ans. 
]
MJC