Page 201 - ADVANCED MATH F.5

Form Five Form Five

11 10
8. ln cosθ 4sinθ + θ − + c
17 17
3 4 12   
x
+
9. 1n 3 cos x + 2sin x + x − tan − 1  tan  + 1 +  c
FOR ONLINE READING ONLY
2
5 5 5   
1 5
10. x + ln cos x + sin x + c
2 2
3 2
11. ln 2cosθ 5sinθ + θ + + c
13 13
3 37
12. ln 7cos 2x − 2sin 2x − xc+
106 53

x
∫
Integrals of exponential functions of the form a dx where a is a
positive constant
Teaching steps
1. Guide students through discussion to recognize integrals of
this form where x is a variable and a is a constant, a > 0, a ≠ 1.

2. Assist students through discussion to solve integrals of the
form:

x
∫ a dx , where a is a constant.
3. Use Examples 9.56 and 9.57 in the Student’s Book to guide
students to solve integrals of exponential functions. Allow
students to share alternative methods of solving integrals of
exponential functions.
4. Engage students in groups to use scientific calculators and
mathematical softwares to verify the solutions of Examples
9.56 and 9.57 in the Student’s Book. Advise them to share their
findings through presentations or gallery walk.

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Mathematics for Advanced Secondary Schools

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