Exam-style Questions: Integration

1. a) By using the substitution u = 4- sin x, or otherwise, find

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b) Hence, or otherwise, find

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(Marks available: 6)

Answer

Answer outline and marking scheme for question: 1

Give yourself marks for mentioning any of the points below:

a) u = 4 - sin x, therefore du = (-) cos x dx.

Substitute u into the given equation gives:

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Integrating this gives:

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Therefore:

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(4 marks)

b) Use u = 2x, therefore 1/2 du = dx

Substitute u into the given equation and integrating gives:

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(2 marks)

(Marks available: 6)