Trapezoid Rule

To calculate the value of an integral one can approximate the function using a polynomial defined on subintervals. The following formula corresponds to passing a straight line through the points (x_o, y_o), (x₁, y₁) and integrating under the interpolant.

If we combine several such integrals for equally spaced points at a = x_o, a+x = x₁, a+2x = x₂,..., at Nx = x_N, a+(N+1)x = b = x_n+1, we get the trapezoid rule.