- #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 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.
\begin{equation}T\left(G\left(g\right)\right)=\int_{g_{1}}^{g_{2}}G(g)\mathrm{d}g\end{equation}
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.
