2021 ASRJC Promo Q7
2021 ASRJC Promo Q7
9 marks
Promo
- Find \(\frac{\mathrm{d}}{\mathrm{d}x}\left( {{\tan }^{3}}x \right)\).[1]Hence find \(\displaystyle\displaystyle \displaystyle\int{{{\sec }^{4}}x\,\mathrm{d}x}\)[2]
- Find \(\displaystyle\displaystyle \displaystyle\int{\sin x\left( \sin x+\sin 3x \right)\,\,\mathrm{d}x}\).[3]
- For \(p>2\), find the value of \(\displaystyle\displaystyle \displaystyle\int_{0}^{p}{x\left| 2-x \right|\,}\mathrm{d}x\) in terms of \(p\).[3]
Video Solution:
Video solution locked
A free account saves your progress; this video needs tuition enrolment.
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.
Create a free account to practise similar questions.
Answer:(a) \(\frac{\mathrm{d}}{\mathrm{d}x}\left( {{\tan }^{3}}x \right)=3{{\tan }^{2}}x{{\sec }^{2}}x\), \(\displaystyle\int{{{\sec }^{4}}x\,\mathrm{d}x}=\tan x+\frac{1}{3}{{\tan }^{3}}x+c\) (b) \(\frac{1}{2}x-\frac{\sin 4x}{8}+c\) (c) \(\frac{8}{3}+\frac{{{p}^{3}}}{3}-{{p}^{2}}\)
Need help? Join our JC Math tuition classes.
Learn more