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1.8 Integration

1.8 Integration

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Question 279
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

1.8 Integration Questions

  1. A Level
  2. /Maths
  3. /1.8 Integration

438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.

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