Integration by substitutionEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

Integration by substitution is the reverse of which rule?
Steps of substitution?
What do you do to the limits of a definite integral when substituting?
Substitution for \int x\left(x^2+3\right)^4dx?
\int x\left(x^2+3\right)^4dx?
\int\frac{e^x}{1+e^x}\,dx?
If u=2x+1, what is dx and what is x?
If u=\sqrt x, what are x and dx?
If u=\cos x, what is du?
How do you integrate \sin^3x?
Value of \int0^{\pi/2}\sin^3x\,dx?
How can you check a substitution result?

Exam questions on Integration by substitution

Let $I=\int x\left(x^2+3\right)^4\,\mathrm{d}x$ .
Hence find the exact value of $\int_0^1x\left(x^2+3\right)^4\,\mathrm{d}x$ .2 marks
Let $N=\int_0^{\ln2}\frac{e^{x}}{1+e^{x}}\,\mathrm{d}x$ , to be found using the substitution $u=1+e^x$ .
Hence find the exact value of $N$ .2 marks
In this question, use integration by substitution with the substitution given in each part.
Use $u=1-x^2$ to find $\int\frac{x}{\sqrt{1-x^2}}\,\mathrm{d}x$ for $|x|<1$ .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).