In a biochemical model, the rate of increase of a substance's concentration, CCC, with respect to time, ttt, is given by dCdt=12t22t3+A\displaystyle \frac{dC}{dt} = \frac{12t^2}{2t^3 + A}dtdC=2t3+A12t2, where A A\,A is a positive constant.
Find
∫12t22t3+A dt \int \frac{12t^2}{2t^3 + A} \, dt ∫2t3+A12t2dtGiven also that
∫1312t22t3+A dt=ln196 \int_{1}^{3} \frac{12t^2}{2t^3 + A} \, dt = \ln 196 ∫132t3+A12t2dt=ln196find the value of AAA.
864 exam-style questions on Edexcel A Level Maths Integration, 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. Each one has a worked solution and a mark scheme showing where the marks go.