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+21t>−2The 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=ln3x = \ln 3x=ln3 and x=ln6x = \ln 6x=ln6.
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)1dt
Hence find an exact value for this area.
