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 Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions 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, 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.
