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Question 578
i.

Find, in simplest form,

∫3(2x−5)4 dx \int \frac{3}{(2x - 5)^4} \, \mathrm{d}x ∫(2x−5)43​dx
[3]
ii.

A population of bacteria grows at a rate R(t)=82t+1\displaystyle R(t) = \frac{8}{2t + 1}R(t)=2t+18​ million per hour, where t t\,t is the time in hours, t≥0t \ge 0t≥0.

Show, by algebraic integration, that the total growth in the population between t=1t = 1t=1 and t=3t = 3t=3 is ln⁡b \ln b\,lnb million, where b b\,b is a rational constant to be found.

[5]
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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