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+51t>−5The 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=ln6x = \ln 6x=ln6 and x=ln12x = \ln 12x=ln12.
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)1dt
Hence find an exact value for this area.
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions 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), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
