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1.8 Integration

1.8 Integration

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Question 180

The rate of change of the concentration C C\,C of a chemical reagent in a reaction is modeled by the differential equation

dCdt=8tln⁡tC,t>0 \frac{\text{d}C}{\text{d}t} = \frac{8t \ln t}{C}, \quad t > 0 dtdC​=C8tlnt​,t>0

where t t\,t is the time in seconds. Given that the concentration is 6 units when t=1t = 1t=1, solve the differential equation to find an expression for the concentration at any time ttt, giving your answer in the form C2=f(t)C^2 = f(t)C2=f(t).

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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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