- #1
james4321
- 6
- 0
I have a definite integral defined by
\begin{equation}T\left(G\left(g\right)\right)=\int_{g_{1}}^{g_{2}}G(g)\mathrm{d}g\end{equation}
where [itex]G[/itex] is a continuous function of a variable [itex]g[/itex], and [itex]g_{1}[/itex] and [itex]g_{2}[/itex] are known numbers. I want to minimize [itex]T\left(G\left(g\right)\right)[/itex], that is I want to find a continuous function [itex]G=f\left(g\right)[/itex] that makes [itex]T\left(G\left(g\right)\right)[/itex] minimum. Ideally I would differentiate it and equate to zero, but because [itex]T\left(G\left(g\right)\right)[/itex] 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.
\begin{equation}T\left(G\left(g\right)\right)=\int_{g_{1}}^{g_{2}}G(g)\mathrm{d}g\end{equation}
where [itex]G[/itex] is a continuous function of a variable [itex]g[/itex], and [itex]g_{1}[/itex] and [itex]g_{2}[/itex] are known numbers. I want to minimize [itex]T\left(G\left(g\right)\right)[/itex], that is I want to find a continuous function [itex]G=f\left(g\right)[/itex] that makes [itex]T\left(G\left(g\right)\right)[/itex] minimum. Ideally I would differentiate it and equate to zero, but because [itex]T\left(G\left(g\right)\right)[/itex] 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.