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3.6 Integration (A-level only)

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Question 58

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

3.6 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Integration (A-level only)

363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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