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.
438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.