# integral of inverse distribution function [closed]

Can Mathematica solve the following problem? The parameter of interests is $\alpha$. Let $G(y)$ be the distribution function of $y$. (e.g. $G$ is a lognormal distribution function with given parameters.). Let $G^{-1}(T)=y$ be the inverse distribution such that $G(y)=T$.

I want to evaluate an integral: $\int_{0}^{G^{-1}(T/\alpha)}f(y)dG(y)$ to see its shape under different $\alpha$.

How can I visualize this integral?

Many thanks.

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What's $f\phantom{}$? –  Ｊ. Ｍ. May 10 at 13:13
If G is a CDF of a known distribution then Mathematica is likely to know its InverseCDF. –  Sjoerd C. de Vries May 11 at 0:03
Ask not what Mathematica can do for you, but what you can do for Mathematica –  wolfies May 11 at 12:13