Ganitagya Gyanam

 Numerical integration is the process of evaluating a definite integral from a set of tabulated values of the integrand. This process when applied to a function of a single variable, is known as quadrature. in this article, we have discussed Newton-Cote's formula and derived the Trapezoidal rule. In the end, we solved a few examples depending on the Trapezoidal rule and gave a few examples to practice.

A device to draw smooth curves through a given set of points such that the slope and curvature are also continuous along the curves, that is, f(x), f′(x), and f″(x) are continuous on the curves. Such a device was called a spline and plotting of the curve was called spline fitting. The advantage of Cubic  Spline fitting usually provides a better approximation of the behavior of functions that have abrupt local changes. Further, splines perform better than higher-order polynomial approximations.