Question

Derive simpson's 1/3 rule for numerical integration

Answer 1

Answer:

order polynomial, and then integrating the polynomial in the interval of. integration. Simpson's 1/3rd rule is an extension of Trapezoidal rule. where the integrand is approximated by a second order polynomial.

Answer 2

Answer:

Simposn's 1/3 rule

Step-by-step explanation:

Explanation:

Simpson's 1/3 rule is a numerical method that approximates the value of definite integral by using quadratic function.

As we know that ,

$\int\limits^a_b {f(x)} \, dx = \int\limits^a_b {y} \, dx$

Formula of Simpson's 1/3 rule is

$\int_{a=x_n}^{b=x_n}ydx$  = $\frac{h}{3}[(y_{o} +y_{n} ) +4(y_{1} +y_{3}+ y_{5} +.....y_{n-1} )+ 2(y_{2}+ y_{4}+ y_{6} ....y_{n-2} )]$

Where , $h =\frac{b-a}{n}$

 $x_{n} = x_{0} +nh$ and

$y_{n} = \frac{1}{1+x_n^2}$

Note: value of n should be multiple of 2.

Final answer:

Hence , this is the formula of simpson's 1/3 rule .