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1.11 H: Integration

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Question 51
a.

Find ∫(2x−x2)dx\displaystyle\int\left(2x - x^2\right)dx∫(2x−x2)dx.

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b.

Evaluate ∫04(2x−x2)dx\displaystyle\int_0^4\left(2x - x^2\right)dx∫04​(2x−x2)dx.

[2]
c.

Using a sketch, explain why the integral in part (b) does not give the area enclosed between the curve y=2x−x2y = 2x - x^2y=2x−x2 and the xxx-axis.

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Markscheme

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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