0606.14.12: Integrate functions of the form — IGCSE Additional Mathematics 0606 past paper questions

Real questions on 0606.14.12: integrate functions of the form

The newest 10 of 10 written questions. Open one to see it on the real paper.

0606/12 · February/March 2026 · Q8c[4]
A curve has equation $y = x e^{2 x + 1}$ . (c) Use your answer to 8(a) to find $\int x e^{2 x + 1} d x$ .See it on the paper →
0606/23 · October/November 2025 · Q4a(i)[2]
(a) Integrate the following with respect to $x$ . (i) $e^{5 x - 2}$ See it on the paper →
0606/23 · October/November 2025 · Q4a(ii)[2]
4 (a) Integrate the following with respect to $x$ . (ii) $\frac{1}{4 - 3 x}$ where $x < \frac{4}{3}$ See it on the paper →
0606/23 · October/November 2025 · Q4b[3]
(b) Show that $\int_{\frac{π}{3}}^{\frac{π}{2}} sec^{2} (\frac{1}{2} x) d x = 2 (1 - \frac{3}{3})$ See it on the paper →
0606/12 · February/March 2025 · Q12b[4]
12 It is given that $y = x e^{3 x + 2}$ . (b) Hence find $\int x e^{3 x + 2} d x$ .See it on the paper →
0606/13 · May/June 2024 · Q5a[4]
When $e^{2 y}$ is plotted against $x^{3}$ , a straight line graph that passes through the points $(2, 5)$ and $(6.4, 7.2)$ is obtained. (a) Find $y$ in terms of $x .$ See it on the paper →
0606/21 · October/November 2023 · Q3a[3]
(a) Find $\int (4 x + 5 - \frac{1}{2 x + 3}) d x$ .See it on the paper →
0606/12 · February/March 2022 · Q4b[5]
(b) Find $\int_{2}^{5} \frac{2 x + 3}{( 2 x - 1 ) ^{2}} d x$ , giving your answer in the form $a + ln b$ , where $a$ and $b$ are constants.See it on the paper →
0606/22 · February/March 2022 · Q11[7]
7-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper →
0606/11 · May/June 2020 · Q11[8]
11 A curve is such that $\frac{d ^{2} y}{d x ^{2}} = 5 cos 2 x$ . This curve has a gradient of $\frac{3}{4}$ at the point $(- \frac{π}{12}, \frac{5 π}{4})$ . Find the equation of this curve.See it on the paper →

What examiners said

Some excellent solutions were seen to this question, with many candidates able to apply the combinations of problem-solving skills needed to produce an accurate and complete answer. Some candidates made premature approximation errors, often when finding the area of the rectangle, and lost the final accuracy mark. A few candidates omitted to show the integrated expression and this was not condoned...
— Examiner report, February/March 2022, 0606/22 Q11 (Cambridge)