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Question 111

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

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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