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Question 533

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.

a.

Find

∫9t3t2+k dt \int \frac{9t}{3t^2 + k} \, dt ∫3t2+k9t​dt
[2]
b.

Given that the change in temperature between t=0t = 0t=0 and t=2t = 2t=2 is exactly ln⁡125\ln 125ln125 degrees, determine the value of kkk.

[4]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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