Page 185 - ADVANCED MATH F.5

Form Five Form Five

3
15. 1 x − 5 x − 2 2x + 3 2 c 16. t − t − t ++
4
2
tc
5
x
c
17. 11e + 18. y 2 − 2 + c
FOR ONLINE READING ONLY
2 y
1
19. 2sinθ – 2cosθ + c 22. x − 3 1 x − 2 3 x − 2 3 + 1 + c
3 2 2 x
4 5 2
20. sin xc+ 23. ln t + t + 4 + c
3 4 t 2
7 3 1 1 3r 2
21. x + 4 x − 3 sin xc+ 24. −+ + + c
3 2 r 3r 3 2

Techniques of integration
Introduce students to common techniques for integration. Assist them
in identifying the most common techniques of integration which
include integration by substitution, by inspection, by parts, and by
partial fractions.

Integration by substitution method

Teaching steps
1. Guide students to discuss the steps for integrating a given
function by the substitution method in the Student’s Book.
Assist them in using the substitution method to integrate
integrals of the form: dx

∫
(a) (ax b dx± ) n (b) ∫ m (ax b dx± ) n (c) ⌠ ax b±
⌡
∫
∫
(d) sin(ax b dx± ) (e) e ax b± dx , where a and b and constants.
2. Use Examples 9.8 to 9.11 in the student’s Book, to guide
students to find solutions of the integrals by the substitution
method. Engage students to use scientific calculators and
mathematical softwares to verify the answers of the given

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