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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