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+k9twhere 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+k9tdtGiven 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 AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
