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Mathematical problems for self assessment

Sample Problems
INTEGRATION I

 

1. Evaluate the indefinite integrals:

(i) image placeholder

(ii) image placeholder

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

 

2. Evaluate the indefinite integrals:

(i) image placeholder

(ii) image placeholder

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

 

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

[Ans. 15/4]

 

4. Calculate the area bounded by the curves image placeholder and image placeholderover the region image placeholder.

[Ans. 3π ]

 

5. Evaluate the definite integrals:

(i) image placeholder

(ii) image placeholder (Hint: Use integration by parts)

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

 

6. Using integration by parts evaluate the indefinite integral

image placeholder

[Ans. image placeholder]

 

7. Using integration by parts evaluate the definite integral

image placeholder

[Ans. image placeholder ]

 

8. Evaluate the improper integral

image placeholder

[Ans. image placeholder]

 

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

image placeholder

and hence evaluate image placeholder

[Ans. ].