ABSTRACT
Integration is the inverse operation of differentiation. Subtractions followed by divisions in differentiation are counteracted by multiplications followed by additions in integration. Integration of a function over a given limit is equivalent to finding the area of the functional curve between the limit and the axis of the independent variable. The formulas of numerical integration evaluate the function to be integrated at the two extreme limits or end points. If numerical representations are used for the first derivatives, the final error becomes dependent on the finite difference schemes used. It should be remembered that the closed form analytical expressions of definite integrals has many advantages and should be used where possible. The integrand was approximated by straight lines in the Trapezoidal method, whereas Simpson's rule does it by parabolic curves. For the functional values available at discrete points, it may be necessary to smooth data by an appropriate least squares approximation and integrate the resulting regressed function.
