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Simpson's 1/3 Rule

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Simpson’s 1/3 rule is based on approximating the integrand by a second order polynomial .It is an extension of Trapezoidal rule where, the trapezoidal rule was based on approximating the integrand by a first order polynomial, and then integrating the polynomial over interval of integration.

It calculates the value of the area under any curve over a given interval by dividing the area into equal parts. It follows the method similar to integration by parts. It is used to estimate the value of a definite integral.

In order to integrate any function f(x) in the interval (a,b), follow the steps given below:

Ø Select a value for n, which is the number of parts the interval is divided into. Let the value of n be an even number.

Ø Calculate the width, h = (b−a) / n.

Ø Calculate the values of x0 to xn as x0 = a, x1 = x0+ h, x n-1 = xn-2 + h, xn = b.

Ø Consider y = f(x). Now find the values of y (y0 to yn) for the corresponding x(x0 to xn) values.

Ø Substitute all the above found values in the Simpson's Rule Formula to calculate the integral value.