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Question 330

The curve C has the parametric equations

x=ln⁡(t+3)y=1t+2t>−2 x = \ln(t+3) \quad y = \frac{1}{t+2} \quad t > -2 x=ln(t+3)y=t+21​t>−2

A first-quadrant graph of curve C with vertical boundaries at x = ln 3 and x = ln 4 and the region between the curve and x-axis shaded.

The finite region R between by the curve C and the x x\,x axis is bounded by the the lines with equations x=ln⁡3x = \ln 3x=ln3 and x=ln⁡4x = \ln 4x=ln4

a.

Find the values of t t\,t when x=ln⁡3x=\ln 3x=ln3 and when x=ln⁡4x=\ln 4x=ln4

[2]
b.

Show that the area of R is given by the integral ∫011(t+2)(t+3) dt\displaystyle \int_0^1 \frac{1}{(t+2)(t+3)}\,dt∫01​(t+2)(t+3)1​dt

[3]
c.

Hence find an exact value for this area

[5]
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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