Finding Area Under Curve with Stochastic Model

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The discussion focuses on finding the area under an exponential function graph using various methods, including empirical and finite element models. The user is specifically seeking information on stochastic or probability models for this purpose. They emphasize the need for a formula or steps rather than tools like a planimeter. Additional numerical integration methods mentioned include Romberg, adaptive quadrature, and Gauss-Legendre. The inquiry aims to gather resources or guidance on applying the stochastic model for area calculation.
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I have an exponential function graph that was given to me as a question i had to find the points and find three different ways of finding the area under the curve.

I found an Empirical model (finding the formula and integrating from one point to another)

I found a Finite Element model (either using simpson's rule or the trapezoidal rule)

But there seems to be another one called a Stochastic model or probability model.

My question is is there anyone that knows where to find this on the net or knows of it right off the back? I would like to know just the rule or steps and i will do the work myself... thanks
 
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You get some device called a planimeter that is (was) used to determine the area under a graph, or the area of any flat surface.
 
but that has nothing to do with the stochastic model or probability model...

i need a formula or set of steps not a tool...
 
Other numerical integration methods are Rhomberg, adaptive quadrature and Gauss-Legendre.
 

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