The curve C C\,C has the parametric equations
x=ln(t+5)y=1t+4t>−4 x = \ln(t+5) \quad y = \frac{1}{t+4} \quad t > -4 x=ln(t+5)y=t+41t>−4The 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=ln5x = \ln 5x=ln5 and x=ln10x = \ln 10x=ln10.
Show that the area of R R\,R is given by the integral ∫051(t+4)(t+5) dt\displaystyle \int_0^5 \frac{1}{(t+4)(t+5)} \, dt∫05(t+4)(t+5)1dt
Hence find an exact value for this area.
