Integration
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Question 333
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=3x = 3x=3.
a.[1]
Show that the xxx-coordinate of the point where C C\,C crosses the xxx-axis is 15.
b.[7]
Hence show that the exact value of the area of R R\,R is aln2+bln3a \ln 2 + b \ln 3aln2+bln3, where a a\,a and b b\,b are rational constants to be found.
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.