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The value of definite integral sin^4 x (where lower limit 0 and upper limit pi)

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Solution: We have ,

$I=int_0^pisin^4x hspace0.1cmdx$

$I=int_0^pisin^4x hspace0.1cmdx=2int_0^pi/2sin^4xhspace0.1cmdx$

$Rightarrow I=(Gamma frac52Gamma frac12)/2Gamma 2=frac3pi8.$

$ecause$ $Gamma frac12=sqrtpi$

Posted by

Deependra Verma

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