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1.8.2 Integrating x^n

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Question 46
i.

Find

∫(3w+2)24w dw,w>0 \int \frac{(3w+2)^2}{4\sqrt{w}} \, dw, \quad w > 0 ∫4w​(3w+2)2​dw,w>0

giving your answer in simplest form.

[4]
ii.

The concentration C C\,C of a chemical in a solution, measured in mol/L, changes over time t t\,t seconds according to the model C=f(t)C = f(t)C=f(t).

It is given that:

  • f′(t)=t2+kt+mf'(t) = t^2 + kt + mf′(t)=t2+kt+m, where k k\,k and m m\,m are constants.
  • The initial concentration of the chemical is 12 mol/L.
  • At t=3t = 3t=3, the concentration is 18 mol/L.
  • At t=3t = 3t=3, the rate of change of the concentration is 2 mol/L/s.

Find f(t)f(t)f(t) in simplest form.

[6]

1.8.2 Integrating x^n Questions

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  3. /1.8.2 Integrating x^n