Page 184 - ADVANCED MATH F.5

Form Five Form Five

∫
(i) ∫ af ()x dx = a f ()x dx
∫
∫
(ii) [af ()x ± bg ()x ]dx = a f ()x dx b g± ∫ ()x dx where a
and b are constants.
13. 6xx− FOR ONLINE READING ONLY
2. Use Examples 9.4 to 9.7 in the Student’s Book to guide
students to find the solution of some simple functions of the
given integrals following all procedures as indicated in the
Student’s Book. Engage students to use scientific calculators
and mathematical software to verify the answers of the given
examples. Advise them to share their findings for more inputs
3. Require students to attempt Exercise 9.2 in the student’s Book.
Advise them to submit their work; check the correctness of
their answers, and provide them constructive feedback.

Answers to Exercise 9.2

5 8 3 1 5 7
1. 4 x + 4 3 x − 3 2 x + 2 5xc+ 5. 12 x + 4 3 x − 3 2 x + 2 2xc+

3 1 2
2. − x + 4 3x + 3 2x − 2 3xc+ 6. − t − t + 7ln t ++
5
−
2
tc
2 2 5
2 5 1 3 6 5 2 7
3. x + 2 x + 2 3xc+ 7. 2x − 2 2x + 2 x − 2 x + 2 c
5 5 7
3
4. 48 t − 7 4 18 t + 7 2 c 8. −+ sin x + c
7 7 x 2
9. 2 x + 3 2 2 x + 1 2 c 10. 8ln x + 5 − 3 + c
3 3 x x 2

5 2 cos x sin x
11. ln t + t + 4 + c 12. ln x − − + c
4 t 2 5 3
2 + c 14. 1 x + 2x ++
2
3
xc
3
178
Mathematics for Advanced Secondary Schools

30/06/2024 18:02:47
ADVANCED MATH F.5 TG CHAPTERS.indd 178
ADVANCED MATH F.5 TG CHAPTERS.indd 178 30/06/2024 18:02:47