English is my second language:
I want to increase the accuracy of the trapezoidal rule for approximating the area beneath a curve by increasing the number of trapeziums the area is segregated into.
My problem is I have very limited knowledge of how to use the sigma function. This is what I have so far:
Area of trapezium = lim(Δx->0) 1/2*Δx*(f(x)+f(x+Δx)) where f(x) is some function of x.
My justification is that by making the Δx very small, the area must be segregated into more trapeziums but I know that this is only half of the solution that I desire - how do I fit this into a sigma function and what constraints do I use?