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3.7 Integration (A-level only)

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Question 104

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.

a.

Find

∫12t22t3+A dt \int \frac{12t^2}{2t^3 + A} \, dt ∫2t3+A12t2​dt
[2]
b.

Given also that

∫1312t22t3+A dt=ln⁡196 \int_{1}^{3} \frac{12t^2}{2t^3 + A} \, dt = \ln 196 ∫13​2t3+A12t2​dt=ln196

find the value of AAA.

[5]
Markscheme

3.7 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.7 Integration (A-level only)

221 exam-style questions on WJEC A Level Maths 3.7 Integration (A-level only), covering 3.7.1 Integration (A-level only), 3.7.2 Integration (A-level only), 3.7.3 Integration (A-level only), 3.7.4 Integration (A-level only), 3.7.5 Integration (A-level only), and 3.7.6 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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