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.
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.