Pure definite integration

Evaluate a definite integral of polynomial, rational, or power functions using the fundamental theorem of calculus, with no applied context.

18 questions · Easy -1.1

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Edexcel C12 2016 January Q3
5 marks Easy -1.2
3. Find, using calculus and showing each step of your working, $$\int _ { 1 } ^ { 4 } \left( 6 x - 3 - \frac { 2 } { \sqrt { x } } \right) \mathrm { d } x$$
Edexcel C2 2009 June Q1
5 marks Moderate -0.8
  1. Use calculus to find the value of
$$\int _ { 1 } ^ { 4 } ( 2 x + 3 \sqrt { } x ) d x$$
Edexcel C2 Q2
5 marks Easy -1.3
2. (a) Find \(\quad \int \left( 3 + 4 x ^ { 3 } - \frac { 2 } { x ^ { 2 } } \right) \mathrm { d } x\).
(b) Hence evaluate \(\quad \int _ { 1 } ^ { 2 } \left( 3 + 4 x ^ { 3 } - \frac { 2 } { x ^ { 2 } } \right) \mathrm { d } x\).
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OCR C2 2007 June Q6
8 marks Moderate -0.8
6
    1. Find \(\int x \left( x ^ { 2 } - 4 \right) d x\)
    2. Hence evaluate \(\int _ { 1 } ^ { 6 } x \left( x ^ { 2 } - 4 \right) d x\).
  2. Find \(\int \frac { 6 } { x ^ { 3 } } d x\)
OCR MEI C2 2006 June Q4
5 marks Easy -1.2
4 Find \(\int _ { 1 } ^ { 2 } \left( x ^ { 4 } - \frac { 3 } { x ^ { 2 } } + 1 \right) \mathrm { d } x\), showing your working.
OCR MEI C2 2009 June Q2
4 marks Easy -1.2
2 Find \(\int _ { 1 } ^ { 2 } \left( 12 x ^ { 5 } + 5 \right) \mathrm { d } x\).
OCR MEI C2 Q6
5 marks Easy -1.2
6 Evaluate \(\int _ { 1 } ^ { 2 } \left( x ^ { 2 } + \frac { 1 } { x ^ { 2 } } \right) \mathrm { d } x\).
OCR MEI C2 Q4
3 marks Easy -1.2
4 Find \(\int _ { 2 } ^ { 5 } \left( 2 x ^ { 3 } + 3 \right) \mathrm { d } x\).
OCR MEI C2 Q6
4 marks Moderate -0.8
6 Find \(\int _ { 2 } ^ { 5 } \left( 1 - \frac { 6 } { x ^ { 3 } } \right) \mathrm { d } x\).
OCR MEI C2 Q7
4 marks Easy -1.2
7 Find \(\int _ { 1 } ^ { 2 } \left( 12 x ^ { 5 } + 5 \right) \mathrm { d } x\).
OCR MEI C2 Q10
5 marks Moderate -0.8
10 Find \(\int _ { 1 } ^ { 2 } \left( \begin{array} { l l } x ^ { 4 } & \frac { 3 } { x ^ { 2 } } + 1 \end{array} \right) \mathrm { d } x\), showing your working.
OCR MEI C2 2011 June Q1
3 marks Easy -1.2
1 Find \(\int _ { 2 } ^ { 5 } \left( 2 x ^ { 3 } + 3 \right) \mathrm { d } x\).
Edexcel C2 Q1
4 marks Moderate -0.8
  1. Evaluate
$$\int _ { 2 } ^ { 4 } \left( 2 - \frac { 1 } { x ^ { 2 } } \right) \mathrm { d } x$$
Edexcel C2 Q1
5 marks Moderate -0.8
  1. Evaluate
$$\int _ { - 2 } ^ { 0 } ( 3 x - 1 ) ^ { 2 } \mathrm {~d} x .$$
Edexcel C2 Q1
4 marks Moderate -0.8
  1. Evaluate
$$\int _ { 1 } ^ { 4 } \left( x ^ { 2 } - 5 x + 4 \right) d x .$$
OCR MEI C2 2010 June Q5
4 marks Moderate -0.8
5 Find \(\int _ { 2 } ^ { 5 } \left( 1 - \frac { 6 } { x ^ { 3 } } \right) \mathrm { d } x\).
AQA Paper 2 2023 June Q2
1 marks Easy -1.8
2 It is given that $$\int _ { 0 } ^ { 6 } \mathrm { f } ( x ) \mathrm { d } x = 20 \text { and } \int _ { 3 } ^ { 6 } \mathrm { f } ( x ) \mathrm { d } x = - 10$$ Find the value of \(\int _ { 0 } ^ { 3 } \mathrm { f } ( x ) \mathrm { d } x\) Circle your answer. \(- 30 - 101030\)
AQA Paper 3 2020 June Q1
1 marks Easy -1.8
1 Given that $$\int _ { 0 } ^ { 10 } \mathrm { f } ( x ) \mathrm { d } x = 7$$ deduce the value of $$\int _ { 0 } ^ { 10 } ( \mathrm { f } ( x ) + 1 ) \mathrm { d } x$$ Circle your answer.
-3
7
8
17