Math Topic · A-Level Maths

Integration

Real exam questions on integration, filterable by calculator use and difficulty, with the official question and mark-scheme PDFs.

65 exam questionsQuestion + answer PDFs
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1
Calculator: YesDifficulty: Medium
JUNE 18 AS Paper 1 · 4 marks · Question 1
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2
Calculator: YesDifficulty: Easy
JUNE 18 AS Paper 2 · 1 marks · Question 1
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3
Calculator: YesDifficulty: Easy
JUNE 18 C12 · 1 marks · Question 1a
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4
Calculator: YesDifficulty: Medium
JUNE 18 C12 · 4 marks · Question 1b
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5
Calculator: YesDifficulty: Easy
JAN 18 C12 · 3 marks · Question 1b
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6
Calculator: YesDifficulty: Medium
JUNE 18 C34 · 3 marks · Question 1i
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7
Calculator: YesDifficulty: Medium
JUNE 18 C34 · 3 marks · Question 1ii
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8
Calculator: YesDifficulty: Medium
JUNE 17 C34 · 6 marks · Question 2
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9
Calculator: YesDifficulty: Medium
JUNE 18 A2 Paper 1 · 3 marks · Question 2i
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10
Calculator: YesDifficulty: Easy
JUNE 18 A2 Paper 1 · 1 marks · Question 2ii
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11
Calculator: YesDifficulty: Easy
JUNE 18 A2 Paper 2 · 1 marks · Question 3
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12
Calculator: YesDifficulty: Easy
OCT 18 C12 · 4 marks · Question 3b
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13
Calculator: YesDifficulty: Medium
OCT 17 C12 · 3 marks · Question 3b
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14
Calculator: YesDifficulty: Easy
JUNE 18 AS Paper 1 · 5 marks · Question 4ii
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15
Calculator: YesDifficulty: Easy
JUNE 18 AS Paper 2 · 4 marks · Question 5
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16
Calculator: YesDifficulty: Medium
JAN 18 C34 · 4 marks · Question 5b
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17
Calculator: YesDifficulty: Medium
OCT 18 C34 · 3 marks · Question 5bi
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18
Calculator: YesDifficulty: Hard
OCT 18 C34 · 3 marks · Question 5bii
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19
Calculator: YesDifficulty: Medium
OCT 17 C34 · 3 marks · Question 5i
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20
Calculator: YesDifficulty: Medium
JUNE 18 A2 Paper 3 · 5 marks · Question 5i
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21
Calculator: YesDifficulty: Hard
OCT 17 C34 · 5 marks · Question 5ii
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22
Calculator: YesDifficulty: Easy
JUNE 18 A2 Paper 3 · 2 marks · Question 5iii
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23
Calculator: YesDifficulty: Easy
OCT 17 C34 · 1 marks · Question 6a
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24
Calculator: YesDifficulty: Medium
OCT 18 C12 · 3 marks · Question 6b
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25
Calculator: YesDifficulty: Medium
OCT 17 C34 · 3 marks · Question 6b
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26
Calculator: YesDifficulty: Easy
JUNE 18 A2 Paper 1 · 3 marks · Question 6c
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27
Calculator: YesDifficulty: Hard
JUNE 18 A2 Paper 2 · 7 marks · Question 7
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28
Calculator: YesDifficulty: Hard
JUNE 18 A2 Paper 2 · 8 marks · Question 7
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29
Calculator: YesDifficulty: Medium
JUNE 18 A2 Paper 1 · 4 marks · Question 7a
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30
Calculator: YesDifficulty: Hard
JUNE 18 A2 Paper 1 · 3 marks · Question 7b
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31
Calculator: YesDifficulty: Hard
JUNE 18 AS Paper 2 · 9 marks · Question 8
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32
Calculator: YesDifficulty: Hard
OCT 17 C34 · 8 marks · Question 8
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33
Calculator: YesDifficulty: Medium
JUNE 17 C34 · 3 marks · Question 8a
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34
Calculator: YesDifficulty: Easy
JUNE 17 C12 · 3 marks · Question 8a
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35
Calculator: YesDifficulty: Medium
JUNE 18 A2 Paper 3 · 6 marks · Question 8b
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36
Calculator: YesDifficulty: Medium
JUNE 17 C12 · 2 marks · Question 8b
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37
Calculator: YesDifficulty: Medium
OCT 18 C34 · 3 marks · Question 8i
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38
Calculator: YesDifficulty: Medium
OCT 18 C34 · 3 marks · Question 8iia
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39
Calculator: YesDifficulty: Hard
OCT 18 C34 · 4 marks · Question 8iib
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40
Calculator: YesDifficulty: Easy
JUNE 18 C34 · 2 marks · Question 9a
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41
Calculator: YesDifficulty: Medium
OCT 17 C12 · 4 marks · Question 9b
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42
Calculator: YesDifficulty: Hard
OCT 17 C12 · 2 marks · Question 9ci
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43
Calculator: YesDifficulty: Hard
OCT 17 C12 · 2 marks · Question 9cii
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44
Calculator: YesDifficulty: Hard
OCT 18 C12 · 6 marks · Question 10c
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45
Calculator: YesDifficulty: Medium
JUNE 18 C12 · 6 marks · Question 11a
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46
Calculator: YesDifficulty: Hard
OCT 17 C34 · 6 marks · Question 11a
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47
Calculator: YesDifficulty: Medium
OCT 17 C34 · 7 marks · Question 11b
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48
Calculator: YesDifficulty: Hard
JUNE 18 C34 · 7 marks · Question 11b
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49
Calculator: YesDifficulty: Medium
OCT 17 C34 · 1 marks · Question 11c
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50
Calculator: YesDifficulty: Hard
JUNE 18 A2 Paper 1 · 10 marks · Question 12
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51
Calculator: YesDifficulty: Hard
OCT 18 C34 · 5 marks · Question 12c
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52
Calculator: YesDifficulty: Hard
JUNE 17 C12 · 6 marks · Question 12c
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53
Calculator: YesDifficulty: Hard
JUNE 18 A2 Paper 1 · 7 marks · Question 13
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54
Calculator: YesDifficulty: Hard
JUNE 18 A2 Paper 2 · 10 marks · Question 13
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55
Calculator: YesDifficulty: Medium
JAN 18 C34 · 3 marks · Question 13a
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56
Calculator: YesDifficulty: Hard
JAN 18 C34 · 3 marks · Question 13b
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57
Calculator: YesDifficulty: Hard
JAN 18 C34 · 2 marks · Question 13c
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58
Calculator: YesDifficulty: Medium
JAN 18 C12 · 8 marks · Question 14b
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59
Calculator: YesDifficulty: Medium
JUNE 17 C34 · 6 marks · Question 14c
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60
Calculator: YesDifficulty: Hard
JUNE 17 C34 · 3 marks · Question 14d
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61
Calculator: YesDifficulty: Hard
JUNE 18 AS Paper 1 · 10 marks · Question 15
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62
Calculator: YesDifficulty: Hard
JUNE 18 C12 · 6 marks · Question 15a
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63
Calculator: YesDifficulty: Hard
JUNE 18 C12 · 3 marks · Question 15b
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64
Calculator: YesDifficulty: Easy
JUNE 18 C12 · 1 marks · Question 15c
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65
Calculator: YesDifficulty: Medium
OCT 17 C12 · 6 marks · Question 15d
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SUBTOPICS
(ax+b)<sup>n</sup> typesApplications of Integration – ArcsApplications of Integration – Surface area of revolutionApplications of Integration – Area bound by a curveApplications of Integration – Volumes of revolutionArea Under a GraphDefinite IntegrationDeriving and using reduction formulaeEquations of CurvesIntegrals involving Partial fractionsIntegrals of Trigonometric FunctionsIntegrating Products of the form f[g(x)]g'(x) by inspectionIntegration as a limit of a sumIntegration by PartsIntegration by SubstitutionIntegration – Common FunctionsIntegration – IntroductionMixed Examples & Exam Question – IntegrationNumerical IntegrationStandard Integrals Involving Hyperbolic FunctionsStandard Integrals Involving Inverse Trigonometric FunctionsThe Weierstrass substitution

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