Integration
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Question 435
The curve C has the parametric equations
x=ln(t+2)y=1t+1t>−1 x = \ln(t+2) \quad y = \frac{1}{t+1} \quad t > -1 x=ln(t+2)y=t+11t>−1
The finite region R between the curve C and the x x\,x axis is bounded by the lines with equations x=ln2x = \ln 2x=ln2 and x=lnkx = \ln kx=lnk, where k>2k>2k>2.
a.[4]
Show that the area of R is given by the integral ∫0k−21(t+1)(t+2) dt\displaystyle \int_0^{k-2} \frac{1}{(t+1)(t+2)}\,dt∫0k−2(t+1)(t+2)1dt
b.[6]
Given that the area of R is ln32\displaystyle \ln\frac{3}{2}ln23, hence find the equation of the line x=lnkx=\ln kx=lnk
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.