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3.6 Integration (A-level only)

3.6 Integration (A-level only)

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Question 24
a.

Express 1(1+2x)(1−x)\frac{1}{(1+2x)(1-x)}(1+2x)(1−x)1​ in partial fractions.

[3]
b.

Hence find the solution of the differential equation

(1+2x)(1−x)dydx=tan⁡y (1+2x)(1-x)\frac{dy}{dx} = \tan y (1+2x)(1−x)dxdy​=tany

for the interval −12<x<710\displaystyle -\frac{1}{2} < x < \frac{7}{10}−21​<x<107​, given that y=π6\displaystyle y = \frac{\pi}{6}y=6π​ when x=0x = 0x=0.

Give your answer in the form sin⁡ny=f(x)\sin^n y = f(x)sinny=f(x) where n n\,n is an integer to be found.

[7]
Markscheme

3.6 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Integration (A-level only)

363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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