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Question 144

A sketch of the curve y = 10x − x² and the line y = kx on x- and y-axes, with the finite region between them shaded.

The sketch shows the curve y=10x−x2y = 10x - x^2y=10x−x2 and the straight line y=kxy = kxy=kx, where 0<k<100<k<100<k<10

a.

Find, in terms of kkk, the coordinates of the points where the line intersects the curve.

[2]
b.

Find, in terms of kkk, the exact 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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