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.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 100 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) 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.