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1.11 H: Integration

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Question 91
a.

Using the substitution u=3x+1u = \sqrt{3x+1}u=3x+1​, show that

∫1512x+4e3x+1 dx \int_{1}^{5} \sqrt{12x+4} e^{\sqrt{3x+1}} \, dx ∫15​12x+4​e3x+1​dx

may be expressed in the form

∫abku2eu du \int_{a}^{b} k u^2 e^u \, du ∫ab​ku2eudu

where aaa, bbb and kkk are constants to be found.

[4]
b.

Hence find, by algebraic integration, the exact value of

∫1512x+4e3x+1 dx \int_{1}^{5} \sqrt{12x+4} e^{\sqrt{3x+1}} \, dx ∫15​12x+4​e3x+1​dx

giving your answer in simplest form.

[4]
Markscheme

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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