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Question

Obtain the reduction formula for π/20sinnxdx for an integer n2.

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Solution

Let In=π20sinnxdx=π20sinn1xsinxdx
now do integration by parts , we get In=sinn1x(cosx)+π20(n1)cos2xsinn2x=0+(n1)π20sinn2x(1sin2x)

=(n1)In2(n1)In
nIn=(n1)In2

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