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1.11 H: Integration

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Question 69

The rate of mass accumulation of a certain chemical product in a reaction, RRR in grams per minute, is modeled by the function

R(t)=10t−152t2−5t,t>2.5 R(t) = \frac{10t - 15}{2t^2 - 5t}, \quad t > 2.5 R(t)=2t2−5t10t−15​,t>2.5

where ttt is the time in minutes since the reaction began.

a.

Express R(t)R(t)R(t) in partial fractions.

[3]
b.

Hence find ∫R(t) dt\int R(t) \, dt∫R(t)dt.

[3]
c.

Use your answer to part (b) to find the value of the constant kkk for which

∫k2kR(t) dt=ln⁡72 \int_k^{2k} R(t) \, dt = \ln 72 ∫k2k​R(t)dt=ln72
[4]
Markscheme

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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