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3.6 Integration (A-level only)

3.6 Integration (A-level only)

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Question 266

The figure shows

  • the curve CCC with equation y=2x−x2y = 2x - x^2y=2x−x2
  • the line lll with equation y=mxy = mxy=mx, where mmm is a constant and 0<m<20 < m < 20<m<2

The line and the curve intersect at the origin OOO and at the point PPP.

Coordinate diagram showing the parabola C, the line l through O and P, and hatched regions R1 and R2.

a.

Find, in terms of mmm, the coordinates of PPP.

[2]
b.

The region R1R_1R1​, shown shaded in the figure, is bounded by CCC and lll.

Show that the area of R1R_1R1​ is

(2−m)36 \frac{(2 - m)^3}{6} 6(2−m)3​
[3]
c.

The region R2R_2R2​, also shown shaded in the figure, is bounded by CCC, the xxx-axis and lll. Given that the area of R1R_1R1​ is equal to the area of R2R_2R2​,

find the exact value of mmm.

[3]
Markscheme

3.6 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Integration (A-level only)

363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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