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Mathematical problems for self assessment

Sample Problems
INTEGRATION II

 

1. By making an appropriate substitution in each case evaluate the integrals:

(i) image placeholder

(ii) image placeholder

(iii) image placeholder

[Ans. (i) image placeholder (ii) image placeholder (iii) image placeholder]

 

2. By making the substitution image placeholder evaluate the indefinite integral

image placeholder

[Ans.image placeholder]

 

3. By making the substitution image placeholderevaluate the indefinite integral

image placeholder

[Ans.image placeholder or image placeholder]

 

4. By completing the square evaluate the following integrals

(i) image placeholder

(ii) image placeholder

[Ans. (i) image placeholder (ii) Ans. image placeholder ]

 

5. Evaluate the indefinite integrals:

(i) image placeholder

(ii) image placeholder

[Ans. (i) image placeholder (ii) image placeholder]

 

6. Evaluate the integrals:

(i) image placeholder

(ii) image placeholder

(iii) image placeholder

[Ans.(i) image placeholder (ii) image placeholder (iii) image placeholder]

 

7. Using partial fractions evaluate the definite integrals:

(i) image placeholder

(ii) image placeholder

[Ans.(i) image placeholder (ii) image placeholder]

 

8. Using partial fractions evaluate the indefinite integral

image placeholder

[Ans. image placeholder]