## Friday, November 7, 2008

### IIT JEE Mathematics Study Plan/Guide 26. Indefinite Integrals and Revision Facilitator

Sections in the Chapter

1. Indefinite Integral - Antiderivative – Primitive

2. Integrals of some standard functions

3. Integration – Some standard formulas

a. ∫kf(x)dx =

b. ∫[f(x)± g(x)]dx =

c. d/dx [∫f(x)dx] =

4. Integration by substitution

5. Integrals of the form [f '(x)/f(x)]dx

6. Integrals of the form sin ^m x cos ^n x dx

7. Integrals of the functional form 1/(x²±a²)

8. Integrals of the form [1/(ax²+bx+c)]dx

9. Integrals of the form [1/√(ax²+bx+c)]dx

10. Integrals of the form [(px+q)/(ax²+bx+c)]dx

11. Integrals of the functional form [P(x)/(ax²+bx+c)]dx

12. Integrals of the form [(px+q)/√(ax²+bx+c)]dx

13. Integrals of the functional form [1/(a sin²x + b cos²x +c)]dx

14. Integrals of the functional form [1/(a sin x + b cos x +c)]dx

15. Integrals of the functional form [(a sin x + b cos x)/(c sin x + d cos x)]dx

16. Integrals of [(a sin x+b cos x +c)/(p sin x + q cos x +r)] dx

17. Integration by parts

18. Integral of e^x [f(x)+f'(x)]dx

19. Integrals of e^ax sinbx dx,e^ax cos bx dx

20. Integrals of √(a²±x²) and √(x²-a²)

21. Integrals of the functions of the form √(ax²+bx+c)dx

22. Integrals of the functions of the form (px+q)[√(ax²+bx+c)]dx

23. Integration of Rational Algebraic Functions by Using Partial Fractions

24. Integration of [(x²+1)/(x^4+λx²+1)]dx

25. Integration of Function [G(x)/(P√Q)]dx

Study Plan

Day 1

1. Primitive or Antiderivative

2. Indefinite Integral
Integrals of some standard functions

3. Fundamental Integration Formulas

4. Some standard results on integration

DAy 2

5. Methods of Integration

6. Integrals of the form [f '(x)/f(x)]dx

7. Integrals of the form sin ^m x cos ^n x dx

8. Some Special Integrals - Integrals of the functional form 1/(x²±a²)

Day 3
Objective Type Exercises 1 to 5

9. Integrals of the form [1/(ax²+bx+c)]dx

10. Integrals of the form [1/√(ax²+bx+c)]dx

Day 4
O.T.E.: 6 to 10

11. Integrals of the form [(px+q)/(ax²+bx+c)]dx

12. Integrals of the functional form [P(x)/(ax²+bx+c)]dx

13. Integrals of the form [(px+q)/√(ax²+bx+c)]dx

Day 5

O.T.E. 11 to 15

14. Integrals of the functional form [1/(a sin²x + b cos²x +c)]dx

15. Integrals of the functional form [1/(a sin x + b cos x +c)]dx

16. Alternative Method to evaluate Integrals of the functional form [1/(a sin x + b cos x +c)]dx

Day 6
O.T.E. 16 to 20

17. Integrals of the functional form [(a sin x + b cos x)/(c sin x + d cos x)]dx

18. Integrals of [(a sin x+b cos x +c)/(p sin x + q cos x +r)] dx

Day 7
O.T.E. 21 to 25

19. Integration by parts

20. Integral of e^x [f(x)+f'(x)]dx

21. Integrals of e^ax sinbx dx,e^ax cos bx dx

Day 8
O.T.E. 26 to 30

22. Some important results - Integrals of √(a²±x²) and √(x²-a²)

23. Integrals of the functions of the form √(ax²+bx+c)dx

24. Integrals of the functions of the form (px+q)[√(ax²+bx+c)]dx

Day 9
O.T.E. 31 to 35

25. Integration of Rational Algebraic Functions by Using Partial Fractions

Day 10

O.T.E. 36 to 40
26. Integration of [(x²+1)/(x^4+λx²+1)]dx

27. Integration of some special irrational algebraic functions - Integration of Function [G(x)/(P√Q)]dx

Day 11
O.T.E. 36 to 55

Day 12
Fill in the blanks type exercise 1 to 20

Day 13 to 15 concept revision - Use the revision facilitator below.

Try to recollect relevant points on the topic.

If required right click on the topic and click on open in a new window to read the relevant material.

Close the window and come back.

1. Indefinite Integral - Antiderivative – Primitive

2. Integrals of some standard functions

3. Integration – Some standard formulas

a. ∫kf(x)dx =

b. ∫[f(x)± g(x)]dx =

c. d/dx [∫f(x)dx] =

4. Integration by substitution

5. Integrals of the form [f '(x)/f(x)]dx

6. Integrals of the form sin ^m x cos ^n x dx

7. Integrals of the functional form 1/(x²±a²)

8. Integrals of the form [1/(ax²+bx+c)]dx

9. Integrals of the form [1/√(ax²+bx+c)]dx

10. Integrals of the form [(px+q)/(ax²+bx+c)]dx

11. Integrals of the functional form [P(x)/(ax²+bx+c)]dx

12. Integrals of the form [(px+q)/√(ax²+bx+c)]dx

13. Integrals of the functional form [1/(a sin²x + b cos²x +c)]dx

14. Integrals of the functional form [1/(a sin x + b cos x +c)]dx

15. Integrals of the functional form [(a sin x + b cos x)/(c sin x + d cos x)]dx

16. Integrals of [(a sin x+b cos x +c)/(p sin x + q cos x +r)] dx

17. Integration by parts

18. Integral of e^x [f(x)+f'(x)]dx

19. Integrals of e^ax sinbx dx,e^ax cos bx dx

20. Integrals of √(a²±x²) and √(x²-a²)

21.Integrals of the functions of the form √(ax²+bx+c)dx

22. Integrals of the functions of the form (px+q)[√(ax²+bx+c)]dx

23. Integration of Rational Algebraic Functions by Using Partial Fractions

24. Integration of [(x²+1)/(x^4+λx²+1)]dx

25. Integration of Function [G(x)/(P√Q)]dx

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