Integration
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Question 687
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.
a.[2]
Find, in terms of mmm, the coordinates of PPP.
b.[3]
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)3c.[3]
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.
Integration Questions
864 exam-style questions on Edexcel A Level Maths Integration, 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. Each one has a worked solution and a mark scheme showing where the marks go.