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+A12t2dt
Given also that ∫1312t22t3+A dt=ln196\int_{1}^{3} \frac{12t^2}{2t^3 + A} \, dt = \ln 196∫132t3+A12t2dt=ln196
find the value of AAA.
Practise Edexcel A Level Maths 11.4 Reverse Chain Rule with exam-style questions for A Level Maths. 8 questions, 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.