Math, Mathematics, Science, Numerical Analysis, Integration.
lengths are f(x_r) and f(x_(r+1)) . You can see clearly it is indeed a trapezoid with a height of h(x_(r+1)-x_r) and the length of 2 parallel sides are the length of the lines which are parallel to y axis. Using just normal geometric area formula of trapezoid, we get, Here 1st term represents sum