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Show that int0^pifx(sinx)dx=pi/2int0^pif...

Show that `int_0^pifx(sinx)dx=pi/2int_0^pif(sinx)dxdot`

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The correct Answer is:
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Let `I=int_(0)^(pi)xf(sinx)dx`……………1
`:.I=int_(0)^(pi)(pi-x)f{sinx(pi-x)}dx`
or `I=int_(0)^(pi)(pi-x)f(sinx)dx` ………….2
Thus, adding 1 and 2 we get
`2I=pi int_(0)^(pi)f(sinx)dx`
or `I=(pi)/2int_(0)^(pi)f(sinx)dx`
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