Page 84 - DMTH202_BASIC_MATHEMATICS_II

Unit 5: Definite Integrals by Substitution

2. Out of the two different methods used to evaluate definite integral by substitution, which Notes
one is better to use? Illustrate.
3 /2

.
3. Evaluate   sin x  1 cosx dx by using substitution.
2 3
4. Evaluate  dt by using substitution.
2
1 t  4
3 2
5. Evaluate 9 x dx  by using substitution.
1 
1 4
0 
6. Evaluate x   5 dx by using substitution.
1 3
7. Evaluate 1  1 x dx  by using substitution.

 /2
8. Evaluate 0  cos 1 x dx  by using substitution.
0 3 4 3
9. Evaluate 1  x 1 2x  dx by using substitution.

4
10. Evaluate 1  2x  1 dx by using substitution.

Answers: Self Assessment

1. indefinite 2. similar
g   b
3.  f   u du 4. False
g   a
5. True 6. original
7. translate 8. limit
9. wrong 10. first
11. substitution 12. complex number

13. division by zero 14. False
15. True

5.6 Further Readings

Books Douglas S. Kurtz, Jaroslav Kurzweil, Charles Swartz, Theories of Integration,
World Scientific.
G. H. Hardy, T. W. Körner, A Course of Pure Mathematics, Cambridge University
Press.

Morris Kline, Calculus: an Intuitive and Physical Approach, Courier Dover
Publications.
Ron Larson, David C. Falvo, Calculus: an Applied Approach, Cengage Learning.

Online link tutorial.math.lamar.edu/Classes/CalcI/SubstitutionRuleDefinite.aspx

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