Integration by partsEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

Integration by parts formula?
Which rule does integration by parts reverse?
How do you choose u?
\int xe^{2x}\,dx?
\int\ln x\,dx?
How do you start \int\ln x\,dx?
\int x^2\ln x\,dx?
\int x\sin2x\,dx?
Definite integral by parts?
How many applications for \int x^2e^{3x}\,dx?
\int1^e\ln x\,dx?
Is a reduction formula needed for A Level Mathematics?

Exam questions on Integration by parts

Let $I=\int xe^{2x}\,\mathrm{d}x$ , to be found by integration by parts.
Hence find the exact value of $\int_0^1xe^{2x}\,\mathrm{d}x$ .2 marks
Integration by parts uses $\int u\frac{\mathrm{d}v}{\mathrm{d}x}\,\mathrm{d}x=uv-\int v\frac{\mathrm{d}u}{\mathrm{d}x}\,\mathrm{d}x$ .
Find $\int x^2\ln x\,\mathrm{d}x$ for $x>0$ .2 marks
In this question, use integration by parts.
Find $\int x\sin2x\,\mathrm{d}x$ .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).