Integration by partsAQA A-Level Maths: Flashcards

What these 12 flashcards ask

Write the integration by parts formula.
Which rule does it reverse?
What should u do when differentiated?
\int xe^{2x}dx?
\int x\cos x\,dx?
\int\ln x\,dx?
How do you integrate \ln x by parts?
For \int x^2\ln x\,dx, choose?
\int x^2e^xdx?
How many applications for \int x^3e^x\,dx?
Definite integral by parts: where do the limits go?
Values to remember at the limits?

Exam questions on Integration by parts

Let $I=\int x\,e^{2x}\,dx$ .
Hence find the exact value of $\int_0^1x\,e^{2x}\,dx$ .2 marks
A student tries to find $\int x\cos x\,dx$ by integration by parts, choosing $u=\cos x$ and $\frac{dv}{dx}=x$ .
Hence find the exact value of $\int_0^{\pi/2}x\cos x\,dx$ .2 marks
The function $y=\ln x$ is defined for $x>0$ .
Use integration by parts with $u=\ln x$ to show that $\int\ln x\,dx=x\ln x-x+c$ .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).