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.
363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.