Edexcel IAL P2 Integration (definite integrals and area) Questions
Definite integrals; area under a curve and between a curve and a line; the trapezium rule.
- P2 · Pure Mathematics 2
- Calculator allowed
- 33 practice questions
What the questions test
The 33 P2 integration (definite integrals and area) practice questions cover:
Worked example 1
Find the exact total area of the finite regions bounded by the curves $y = x^3 + x^2$ and $y = 2x^2 + 2x$.
Mark scheme
- M1 for setting $x^3 + x^2 = 2x^2 + 2x \implies x^3 - x^2 - 2x = 0$.
- M1 for factoring $x(x-2)(x+1)=0$ to find the intersection points $x=-1, 0, 2$.
- M1 for recognising two distinct regions and setting up integrals: $\int_{-1}^{0} (x^3 - x^2 - 2x) \, dx$ and $\int_{0}^{2} (2x^2 + 2x - x^3 - x^2) \, dx$.
- M1 for integrating the generic polynomial to $\pm[\frac{x^4}{4} - \frac{x^3}{3} - x^2]$.
- M1 for evaluating the area of the first region to $\frac{5}{12}$.
- M1 for evaluating the area of the second region to $\frac{8}{3}$.
- A1 for calculating the combined total area: $\frac{5}{12} + \frac{8}{3} = \frac{37}{12}$.
Worked example 2
The curve with equation $y = x^3 - 4x$ intersects the x-axis at $x = -2$, $x = 0$, and $x = 2$. Find the total exact area enclosed between the curve and the x-axis.
Mark scheme
- M1 for recognising that the region between $0$ and $2$ is below the x-axis, so the integrals must be computed separately.
- M1 for integrating to find the generic primitive: $[\frac{1}{4}x^4 - 2x^2]$.
- M1 for evaluating the integral from $-2$ to $0$: $(0) - (4 - 8) = 4$.
- M1 for evaluating the integral from $0$ to $2$: $(4 - 8) - (0) = -4$.
- M1 for taking the absolute value of the negative area before combining.
- A1 for the total correct area: $4 + |-4| = 8$.
FAQ
What integration (definite integrals and area) is in Edexcel IAL P2?
Definite integrals; area under a curve and between a curve and a line; the trapezium rule.
Is P2 a calculator paper?
Yes, a calculator is allowed in P2, but method marks are only given for working you write down.
How are P2 integration (definite integrals and area) 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.