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Question 653
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]
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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