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Question 624
a.

Use the substitution x=3sin⁡ux = 3 \sin ux=3sinu to show that

∫01.52x+3(9−x2)32 dx=∫0p(23sec⁡utan⁡u+13sec⁡2u) du \int_{0}^{1.5} \frac{2x+3}{(9-x^2)^{\frac{3}{2}}} \, dx = \int_{0}^{p} \left( \frac{2}{3} \sec u \tan u + \frac{1}{3} \sec^2 u \right) \, du ∫01.5​(9−x2)23​2x+3​dx=∫0p​(32​secutanu+31​sec2u)du

where p p\,p is a constant to be found.

[5]
b.

Hence find the exact value of

∫01.52x+3(9−x2)32 dx \int_{0}^{1.5} \frac{2x+3}{(9-x^2)^{\frac{3}{2}}} \, dx ∫01.5​(9−x2)23​2x+3​dx
[3]
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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