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Question 102

A coordinate sketch showing the curve y = x(6 − x), the horizontal line y = 5, and the shaded region R.

The sketch shows the curve y=x(6−x)y = x(6 - x)y=x(6−x) and the line y=5y = 5y=5

a.

Find the coordinates of the points where the line intersects the curve.

[2]
b.

Show that the area of the shaded region R R\,R is given by

∫15(6x−x2) dx−20. \int_1^5 (6x - x^2)\,dx - 20. ∫15​(6x−x2)dx−20.
[2]
c.

Hence find the area of the shaded region RRR.

[4]
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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