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Question 685
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

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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