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1.11 H: Integration

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Question 86

The curve C C\,C has the parametric equations

x=ln⁡(t+6)y=1t+5t>−5 x = \ln(t+6) \quad y = \frac{1}{t+5} \quad t > -5 x=ln(t+6)y=t+51​t>−5

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⁡6x = \ln 6x=ln6 and x=ln⁡12x = \ln 12x=ln12.

a.

Show that the area of R R\,R is given by the integral ∫061(t+5)(t+6) dt\displaystyle \int_0^6 \frac{1}{(t+5)(t+6)} \, dt∫06​(t+5)(t+6)1​dt

[4]
b.

Hence find an exact value for this area.

[6]
Markscheme

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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