Question

# If the integral of the function sin(lnx)x=f(x), then find the value of f(1) (take constant of integration equal to zero) ___

Solution

## We know the integral of sinx and lnx separately but not of the function sin(lnx). But we have the derivative of lnx in the given function. We will replace lnx with t and proceed t=ln x ⇒dt=dxxSo we get ∫sin(lnx)xdx=∫sin(t)dt=−cost Replacing t with lnx, we get f(x) = - cos (lnx) We want to find f(1) f(1) = - cos(ln(1))       = - cos(0)        = -1  Mathematics

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