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.

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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 $y = 4x - x^2$ . The finite region $R$ , shown shaded, is enclosed by the curve and the $x$ -axis. Find the area of $R$ .
Level 2 · 3 marksTry it
2
In this question you must show detailed reasoning.

The region $R$ is bounded by the curve $y = \dfrac{4}{3x + 2}$ , the line $x = 2$ and the coordinate axes.

Find the exact area of $R$ .

(3 marks)
Level 2 · 3 marksTry it
3
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
4
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
5
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

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