Edexcel IAL P4 Integration Questions
Integration by substitution, by parts and using partial fractions; trig identities in integration; volumes of revolution about the x-axis.
- P4 · Pure Mathematics 4
- Calculator allowed
- 30 practice questions
What the questions test
The 30 P4 integration practice questions cover:
Worked example 1
Using the substitution $u^2 = 2x-1$, find $\int x\sqrt{2x-1} \, dx$.
Mark scheme
- M1 for implicit differentiation $2u \, du = 2 \, dx \implies dx = u \, du$.
- M1 for rearranging the substitution to find $x = \frac{u^2+1}{2}$.
- M1 for substituting everything into the integral: $\int (\frac{u^2+1}{2})(u)(u) \, du$.
- M1 for expanding to $\frac{1}{2} \int (u^4 + u^2) \, du$.
- M1 for integrating to $\frac{1}{10}u^5 + \frac{1}{6}u^3$.
- A1 for replacing $u$ with $(2x-1)^{\frac{1}{2}}$ to get $\frac{1}{10}(2x-1)^{\frac{5}{2}} + \frac{1}{6}(2x-1)^{\frac{3}{2}} + c$.
Worked example 2
Find $\int \frac{x^2+1}{x(x-1)} \, dx$.
Mark scheme
- M1 for recognising the improper fraction and performing division to get $1 + \frac{x+1}{x(x-1)}$.
- M1 for setting up partial fractions for the remainder: $\frac{x+1}{x(x-1)} = \frac{A}{x} + \frac{B}{x-1}$.
- A1 for determining the constants $A = -1$ and $B = 2$.
- M1 for formulating the complete integral: $\int (1 - \frac{1}{x} + \frac{2}{x-1}) \, dx$.
- A1 for integrating the terms correctly to $x - \ln|x| + 2\ln|x-1| + c$.
FAQ
What integration is in Edexcel IAL P4?
Integration by substitution, by parts and using partial fractions; trig identities in integration; volumes of revolution about the x-axis.
Is P4 a calculator paper?
Yes, a calculator is allowed in P4, but method marks are only given for working you write down.
How are P4 integration questions marked?
With M marks for a correct method, A marks for accurate answers that depend on the M mark before them, and B marks for independent results, as in the worked examples on this page.