2022TrialShort answer

Q16 (b) (ii)

2 marks

Question

If
$I_n=\int_0^{\pi/2}\cos^n\theta\,d\theta,$
hence find
$\int_0^{\pi/2}\cos^7\theta\,d\theta.$

Try the question before revealing the answer.

Solution

Q.16(b)(ii)
$I_1=\int_0^{\frac{\pi}{2}}\cos\theta\,d\theta$
$=[\sin\theta]_0^{\frac{\pi}{2}}$
$=1$

$I_7=\frac{6}{7}\times\frac{4}{5}\times\frac{2}{3}\times I_1$
$=\frac{16}{35}$

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Syllabus alignment

Calculus

Further IntegrationApply substitution, partial fractions, integration by parts and recurrence relationships to theoretical and practical problems.

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