Integration
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Question 424
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
Graph of curve C in the first quadrant. The curve is a decreasing curve that passes through (ln2,1)(\ln 2, 1)(ln2,1) and (lnk,1k−1)\displaystyle (\ln k, \frac{1}{k-1})(lnk,k−11). The area under the curve between the x-axis and the curve is shaded with diagonal lines.
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]
Hence find an exact value for this area in terms of kkk
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.