Integration using partial fractionsAQA A-Level Maths: Flashcards

What these 12 flashcards ask

What do partial fractions do?
Form of \frac{px+q}{(x-a)(x-b)}?
How do you find A quickly?
\int\frac{A}{ax+b}dx?
\frac{5x+1}{(x-1)(x+2)} in partial fractions?
\int\frac{5x+1}{(x-1)(x+2)}dx?
\int\frac{2}{2x-1}dx?
Laws: \ln a-\ln b=?
Laws: n\ln a=?
\int\frac{4}{(2x-1)(2x+1)}dx?
Why use modulus signs in \ln|ax+b|?
Area under y=\frac{12}{(x+1)(x+3)} from 0 to 3?

Exam questions on Integration using partial fractions

Let $\frac{5x+1}{(x-1)(x+2)}\equiv\frac{A}{x-1}+\frac{B}{x+2}$ , where $A$ and $B$ are constants.
Hence find the exact value of $\int_2^4\frac{5x+1}{(x-1)(x+2)}\,dx$ , giving your answer in the form $a\ln3+b\ln2$ .2 marks
It is given that $\frac{4}{(2x-1)(2x+1)}\equiv\frac{2}{2x-1}-\frac{2}{2x+1}$ , and $x>\frac12$ .
Hence find the exact value of $\int_1^2\frac{4}{(2x-1)(2x+1)}\,dx$ .2 marks
Let $f(x)=\frac{11x-1}{(x-2)(3x+1)}$ for $x>2$ .
Express $f(x)$ in the form $\frac{A}{x-2}+\frac{B}{3x+1}$ , where $A$ and $B$ are constants to be found.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).