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Question 684
i.

Find

∫e2xex+1 dx \int \frac{e^{2x}}{\sqrt{e^x + 1}} \, dx ∫ex+1​e2x​dx
[5]
ii.

During a chemical reaction, the rate of change of the mass mmm of a byproduct, in grams per hour, is modeled by the equation

dmdt=27t3t+4,t≥0 \frac{dm}{dt} = \frac{27t}{\sqrt{3t + 4}}, \quad t \ge 0 dtdm​=3t+4​27t​,t≥0

Use the substitution u=3t+4u = \sqrt{3t + 4}u=3t+4​ to show that

∫27t3t+4 dt=2(3t+4)12(At+B)+k \int \frac{27t}{\sqrt{3t + 4}} \, dt = 2(3t + 4)^{\frac{1}{2}}(At + B) + k ∫3t+4​27t​dt=2(3t+4)21​(At+B)+k

where AAA and BBB are integers to be found and kkk is a constant of integration.

[7]
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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