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Let f(x)=intx^(sinx)(1+xcosxdotlnx+sinx)...

Let `f(x)=intx^(sinx)(1+xcosxdotlnx+sinx)dxa n df(pi/2)=(pi^2)/4dot` Then the value of `|"cos"(f(pi))|` is____

Text Solution

Verified by Experts

The correct Answer is:
-1
`f(x)=int x^(sinx)(1+xcosx*Inx+sinx)dx`
`"If " F(x)=x^(sinx)=e^(sinx Inx)," then " `
`f(x)=int(F(x)+xF'(x))=xF(x)+C`
`=x*x^(sinx)+C`
`"or " f((pi)/(2))=(pi)/(2)*(pi)/(2)+C " or " C=0`
` :. f(x)=x(x)^(sinx),f(pi)=pi(pi)^(0)=pi`
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