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1.9.27 Integration by substitution (reverse chain rule) (A-level only)

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Question 22

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]

1.9.27 Integration by substitution (reverse chain rule) (A-level only) Questions

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