A scientist models the rate of temperature change, dTdt\frac{dT}{dt}dtdT, of a new alloy using the equation dTdt=9t3t2+k\frac{dT}{dt} = \frac{9t}{3t^2 + k}dtdT=3t2+k9t where t≥0t \ge 0t≥0 is the time in seconds and kkk is a positive constant.
Find ∫9t3t2+k dt\int \frac{9t}{3t^2 + k} \, dt∫3t2+k9tdt
Given that the change in temperature between t=0t = 0t=0 and t=2t = 2t=2 is exactly ln125\ln 125ln125 degrees, determine the value of kkk.
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.