Integration using partial fractionsEdexcel A-Level Further Maths: Flashcards

What these 13 flashcards ask

Form of partial fractions for \frac{1}{(x+k)(ax^2+c)}?
Why is the numerator Bx+C over ax^2+c?
How do you find A for the linear factor (x+k)?
How do you find B and C?
What must be true of a fraction before splitting it?
\int\frac{f'(x)}{f(x)}\,dx?
\int\frac{1}{x^2+a^2}\,dx?
\int\frac{x}{x^2+4}\,dx?
\int\frac{1}{x^2+4}\,dx?
\int\frac{1}{4x^2+9}\,dx?
Why is no modulus needed in \ln(x^2+7)?
How do you integrate \frac{Bx+C}{ax^2+c}?
Value of \arctan1?

Exam questions on Integration using partial fractions

Let $f(x)=\frac{5}{(x+1)(x^2+4)}$ , which is to be written in the form $\frac{A}{x+1}+\frac{Bx+C}{x^2+4}$ .
Given that $A=1$ , find the values of $B$ and $C$ .2 marks
Let $g(x)=\frac{1-x}{x^2+4}$ .
Hence find the exact value of $\int_0^2 g(x)\,dx$ .2 marks
Let $f(x)=\frac{2x^2+17}{(x+2)(4x^2+9)}$ .
Express $f(x)$ in the form $\frac{A}{x+2}+\frac{Bx+C}{4x^2+9}$ , where $A$ , $B$ and $C$ 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).