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3.6 Integration (A-level only)

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Question 3

The curve C C\,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

The finite region R R\,R between the curve C C\,C and the x x\,x axis is bounded by the lines with equations x=ln⁡3x = \ln 3x=ln3 and x=ln⁡6x = \ln 6x=ln6.

a.

Show that the area of R R\,R is given by the integral ∫031(t+2)(t+3) dt\displaystyle \int_0^3 \frac{1}{(t+2)(t+3)} \, dt∫03​(t+2)(t+3)1​dt

[4]
b.

Hence find an exact value for this area.

[6]
Markscheme

3.6 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Integration (A-level only)

363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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