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

Answers (1)

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

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