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3.6 Integration (A-level only)

3.6 Integration (A-level only)

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Question 264
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

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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