Express 1(1+2x)(1−x)\frac{1}{(1+2x)(1-x)}(1+2x)(1−x)1 in partial fractions.
Hence find the solution of the differential equation
(1+2x)(1−x)dydx=tany (1+2x)(1-x)\frac{dy}{dx} = \tan y (1+2x)(1−x)dxdy=tanyfor 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 sinny=f(x)\sin^n y = f(x)sinny=f(x) where n n\,n is an integer to be found.
91 exam-style questions on WJEC A Level Maths 4.6 Integration (A-level only), covering 4.6.1 Integration (A-level only) and 4.6.2 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.