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Question 181
a.

Verify that ∫(2x−x2)dx=x2−13x3+C\displaystyle \int (2x - x^2) dx = x^2 - \frac{1}{3}x^3 + C∫(2x−x2)dx=x2−31​x3+C

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b.

Verify that ∫04(2x−x2)dx=−163\displaystyle \int_0^4 (2x - x^2) dx = -\frac{16}{3}∫04​(2x−x2)dx=−316​

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c.

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

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Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

411 exam-style questions on Edexcel A Level Maths Integration, covering 13.1 Integrating x^n, 13.2 Indefinite Integrals, 13.3 Finding Functions, 13.4 Definite Integrals, 13.5 Areas under Curves, 13.6 Areas under the x-axis, and 13.7 Areas between curves and lines. Each one has a worked solution and a mark scheme showing where the marks go.

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