Page 197 - ADVANCED MATH F.5

Form Five Form Five

2
−
25. tan ( (x − 3 2)) c+ 26. 2s + 9 1 + c
2
1 1
3
2
8(4s + 9) 2
2 1

2
1 x +
27. 7ln x ++  sin − 1 ( 2x )  + sin 2sin − 1 ( 2x )  + c
FOR ONLINE READING ONLY
16   2  
5. Guide students through discussion to recognize integrals
whose solutions are obtained by applying the trigonometric
x
substitutions t = tan x or t = tan .
2
6. Assist students through discussion to solve integrals of the
form:
⌠
(a)  1
2
⌡ ab+ sin x c+ 2 cos x
⌠ 1
(b)  dx
⌡ ab+ sin x c+ cos x

7. In groups, formulate a strategy that will engage students to
perform Examples 9.47 to 9.51 in the Student’s Book. Allow
students to share alternative methods of finding solutions for
the integrals that involve trigonometric substitutions. Engage
students in groups to use mathematical softwares and scientific
calculators to verify solutions for the integrals in the examples
in the Student’s Book. Advise them to share their solutions
through presentations.
8. Direct students to attempt Exercise 9.9 in the Student’s Book.
Advise them to submit their work. Check the correctness
of their answers, and provide them constructive feedback.
Encourage students to explore additional resources, such as
online tutorials, Symbolab, Mathematica, or reference books,
to enrich their understanding and for further practice.

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