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Question 94

A sketch of the curve y = x(x − 1)(x − 2) on coordinate axes, with two regions between the curve and the x-axis shaded.

The sketch shows the curve y=x(x−1)(x−2)y = x(x - 1)(x - 2)y=x(x−1)(x−2)

a.

Write down the values of x x\,x where the curve crosses the x x\,x axis.

[1]
b.

Show that ∫x(x−1)(x−2) dx=14x4−x3+x2\displaystyle \int x(x - 1)(x - 2) \, dx = \frac{1}{4}x^4 - x^3 + x^2∫x(x−1)(x−2)dx=41​x4−x3+x2.

[2]
c.

Find the area of the shaded region.

[6]
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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