A-level · Integration

Areas with integrationExam-style questions

Setting up a definite integral for each kind of area question. A region between a curve and the x-axis, with the limits found from the x-intercepts; a region below the axis, where the integral is negative and the area is its size; a curve that crosses the axis inside the range, split at the crossing; the region between a curve and a line, as top minus bottom between the points where they meet; and regions made of a triangle and a curved piece.

Start practising Read the lesson

29 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
The diagram shows the curve $y = x^2$ and the line $y = x + 2$ . The finite region $R$ , shown shaded, is enclosed by the curve and the line. Find the area of $R$ .
Level 3 · 4 marksTry it
2
The diagram shows the curve $y = x^2 - 4$ . The shaded region $R$ is enclosed between the curve and the $x$ -axis. Find the area of $R$ .
Level 3 · 3 marksTry it
3
The diagram shows the curve $y = 9 - x^2$ . The shaded region $R$ is enclosed between the curve and the $x$ -axis. Find the area of $R$ .
Level 3 · 3 marksTry it
4
The diagram shows the curve $y = x(x - 3)$ , which lies below the $x$ -axis for $0 < x < 3$ . Find the area of the shaded region enclosed between the curve and the $x$ -axis.
Level 3 · 3 marksTry it
5
The diagram shows the curve $y = x^2 - 2x$ and the line $y = x$ . The finite region $R$ , shown shaded, is enclosed by the curve and the line. Find the area of $R$ .
Level 3 · 4 marksTry it

6 more questions on areas with integration

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free