Integration | Cambridge O Level Additional Maths Topic Questions 2025

1

6 marks

Find the exact value of $\int_{2}^{4} \frac{{(x + 1)}^{2}}{x^{2}} d x$ .

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1a

4 marks

Giving your answer in its simplest form, find the exact value of

$\int_{0}^{4} \frac{10}{5 x + 2} d x$

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1b

5 marks

$\int_{0}^{\ln 2} {(e^{4 x + 2})}^{2} d x$

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1a

1 mark

Show that $\frac{1}{x + 1} + \frac{2}{3 x + 10}$ can be written as $\frac{5 x + 12}{3 x^{2} + 13 x + 10}$

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1b

9 marks

q10b-0606-w20-qp-13-additional-maths

The diagram shows part of the curve $y = \frac{5 x + 12}{3 x^{2} + 13 x + 10}$ , the line $x = 2$ and a straight line of gradient 1. The curve intersects the $y$ -axis at the point $P$ . The line of gradient 1 passes through $P$ and intersects the $x$ -axis at the point $Q$ . Find the area of the shaded region, giving your answer in the form $a + \frac{2}{3} \ln (b \sqrt{3})$ , where $a$ and $b$ are constants.

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Integration (Cambridge O Level Additional Maths)

Topic Questions