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Question 56

The curve C, the x-axis and a vertical line at x=k bound region R, with the curve crossing the positive x-axis and continuing briefly below it.

The curve C C\,C with equation y=15−x(2x−3)(x+1)\displaystyle y = \frac{15 - x}{(2x - 3)(x + 1)}y=(2x−3)(x+1)15−x​. The region R R\,R is bounded by the curve CCC, the xxx-axis and the line with equation x=kx = kx=k, where 32<k<15\displaystyle \frac{3}{2} < k < 1523​<k<15.

The exact value of the area of R R\,R is 11310ln⁡3−645ln⁡2\displaystyle \frac{113}{10}\ln 3 - \frac{64}{5}\ln 210113​ln3−564​ln2. Find the value of kkk.

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Markscheme

Integration Questions

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

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.

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