Q63. Let f be a continous, strictly decreasing, real-valued function such that is finite and f(0)=1.

In terms of (the inverse function of f), is:

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I tried using the "Inverse Function Integration method":

Is the method valid?

Also, how do we conclude that xf(x)=0, when x is infinity? (x would be infinity while f(x)=0)

Lastly, is there any faster method?

Thank you very much.