0606.14.11: Integrate sums of terms in powers of x, Solutions for indefinite integrals should inclu…: past paper questions

Real questions on 0606.14.11: integrate sums of terms in powers of x, solutions for indefinite integrals should inclu…

The newest 20 of 26 written questions. Open one to see it on the real paper.

1. 0606/13 · May/June 2026 · Q11[10]

   10-mark question — its maths and diagrams are best seen on the paper.

   See it on the paper →
2. 0606/22 · February/March 2026 · Q10b(i)[3]
   In this question time $t$ is in seconds and displacement $s$ is in metres. For $t⩾0$, a particle moves on the positive $x$-axis. At time $t$ the acceleration of the particle is $2t-9$. At time $t=7$ the velocity of the particle is 4. (b) At time $t=12$, the displacement of the particle from the origin $...See it on the paper →
3. 0606/22 · February/March 2026 · Q10b(ii)[3]
   In this question time $t$ is in seconds and displacement $x$ is in metres. For $t⩾0$, a particle moves on the positive $x$-axis. At time $t$ the acceleration of the particle is $2t-9$. At time $t=7$ the velocity of the particle is 4. (b) At time $t=12$, the displacement of the particle from the origin...See it on the paper →
4. 0606/21 · October/November 2025 · Q8a(iii)[4]
   In this question, the units are metres and seconds. A particle $P$ is travelling in a straight line through a fixed point $O$. At time $t$ its acceleration, $a$, is given by $a=(2t-3{)}^2$, where $t\ge 0$. When $t=3$, $P$ has a velocity of 6. (iii) Find the displacement of $P$ from $O$ when $t=3$.See it on the paper →
5. 0606/12 · May/June 2025 · Q4a[2]
   4 (a) Find ${\int }_0^{\pi }\sin \theta \mathrm{d}\theta$.See it on the paper →
6. 0606/13 · October/November 2024 · Q7b[4]
   (b) Hence find ${\int }_1^{2}3x^2\ln x\mathrm{d}x$, giving your answer in the form $\ln a+b$, where $a$ is an integer and $b$ is a rational number.See it on the paper →
7. 0606/23 · October/November 2024 · Q6a[2]
   6 (a) Find $\int \frac{1}{\sqrt{3x+2}}\mathrm{d}x$.See it on the paper →
8. 0606/23 · October/November 2024 · Q6b[3]
   (b) Find, in terms of $a$, ${\int }_{0.5}^a{\mathrm{e}}^{(1-2x)}\mathrm{d}x$.See it on the paper →
9. 0606/23 · October/November 2024 · Q8b[5]

   5-mark question — its maths and diagrams are best seen on the paper.

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10. 0606/13 · May/June 2024 · Q4[5]
    4 Find ${\int }_0^2{\left(1+{\mathrm{e}}^{2x}\right)}^2\mathrm{d}x$, giving your answer in exact form.See it on the paper →
11. 0606/23 · October/November 2023 · Q4[6]
    4 Find the exact value of ${\int }_3^5\frac{(x-1{)}^2}{x^3}\mathrm{d}x$.See it on the paper →
12. 0606/23 · May/June 2023 · Q3b[2]
    (b) Hence find $\int \frac{x+2}{x(x+3)}\mathrm{d}x$.See it on the paper →
13. 0606/13 · October/November 2022 · Q7[5]
    7 Find the exact value of ${\int }_0^{\frac{\pi }{2}}(\cos 3x+4\sin 2x+1)\mathrm{d}x$.See it on the paper →
14. 0606/13 · May/June 2022 · Q10b[6]
    (b) Hence find the exact value of ${\int }_0^2\frac{14x+10}{(2+3x)(x+1{)}^2}\mathrm{d}x$. Give your answer in the form $p+\ln q$, where $p$ and $q$ are rational numbers.See it on the paper →
15. 0606/23 · May/June 2021 · Q8a(i)[2]
    8 (a) (i) Find $\int \sin \left(\frac{\varphi +\pi }{3}\right)\mathrm{d}\varphi$.See it on the paper →
16. 0606/23 · May/June 2021 · Q8a(ii)[2]
    (ii) Find $\int (5{\sin }^2\theta +5{\cos }^2\theta )\mathrm{d}\theta$.See it on the paper →
17. 0606/23 · May/June 2021 · Q8b[4]
    (b) Show that ${\int }_1^e\left({\left(1+\frac{1}{x}\right)}^2-1\right)\mathrm{d}x=\frac{3\mathrm{e}-1}{\mathrm{e}}$.See it on the paper →
18. 0606/21 · October/November 2020 · Q11b[5]

    5-mark “Find” question — its maths and diagrams are best seen on the paper.

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19. 0606/23 · October/November 2020 · Q7c[5]
    A curve has equation $y=x\cos x$. (c) Using your answer to part (a), find the exact value of ${\int }_0^{\frac{\pi }{6}}x\sin x\mathrm{d}x$.See it on the paper →
20. 0606/13 · May/June 2020 · Q9[8]

    8-mark “Find” question — its maths and diagrams are best seen on the paper.

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What examiners said

Comprehensive responses • Many correct solutions were seen. • Most candidates integrated the velocity function correctly and found the correct value of the constant of integration. Limited responses • Some candidates made arithmetic errors.

— Examiner report, February/March 2026, 0606/22 Q10(b)(i) (Cambridge)

Comprehensive responses • This question part was quite demanding and fewer completely correct solutions were seen. • More successful candidates often drew a sketch and realised they needed to consider the displacements at times when t = 0. 3 and 6. Limited responses • Many candidates did not use a correct method, with many making a substitution of t = 6 into their response to part (b) and not co...

— Examiner report, February/March 2026, 0606/22 Q10(b)(ii) (Cambridge)

A small number of fully correct responses were seen. Some candidates gained partial credit for a correct expression in x with the constant of integration omitted. Weaker responses commonly either incorrectly attempted some algebraic manipulation before they integrated, in an attempt to write the algebraic fraction as powers of x, or applied the quotient rule for differentiation.

— Examiner report, May/June 2023, 0606/23 Q3(b) (Cambridge)