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Question 332

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]

Integration Questions

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

Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank