11.5 Integration by Substitution
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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]

11.5 Integration by Substitution Questions

Practise Edexcel A Level Maths 11.5 Integration by Substitution with exam-style questions for A Level Maths. 59 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

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11.5 Integration by Substitution Questions

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