# Minimizing a functional definite integral

1. Dec 19, 2012

### james4321

I have a definite integral defined by

$$T\left(G\left(g\right)\right)=\int_{g_{1}}^{g_{2}}G(g)\mathrm{d}g$$

where $G$ is a continuous function of a variable $g$, and $g_{1}$ and $g_{2}$ are known numbers. I want to minimize $T\left(G\left(g\right)\right)$, that is I want to find a continuous function $G=f\left(g\right)$ that makes $T\left(G\left(g\right)\right)$ minimum. Ideally I would differentiate it and equate to zero, but because $T\left(G\left(g\right)\right)$ is too complicated to be obtained and then differentiated analytically, I would like to know if there is a numeric technique or any other technique by which this problem can be solved.

2. Dec 19, 2012