Question

In Numerical integration, what Should be the number of intervals to apply simpson's of one third rule?​

Answer 1

Answer:

Simpson's 1/3 rule is an Page 2 07.03.2 Chapter 07.03 extension of Trapezoidal rule where the integrand is approximated by a second order polynomial. xaxaaxf + + = . a and 2 a . Since the above form has 1/3 in its formula, it is called Simpson's 1/3 rule.

The ApproximateInt(f(x), x = a.. b, method = simpson[3/8], opts) command approximates the integral of f(x) from a to b by using Simpson's 3/8 rule. This rule is also known as Newton's 3/8 rule. The first two arguments (function expression and range) can be replaced by a definite integral.

Answer 2

Answer:

The number of intervals to apply Simpson's of one third rule must be a multiple of $2.$

Step-by-step explanation:

Simpson's one-third rule can be used to integrate a function $f(x)$ in the interval $(a,b)$

Make $n$ sections out of the interval. Let $n$ be an even number.

Then width $h=\frac{b-a}{h}$

Calculate the values of $x_{0}$ to $x_{n}$ as $x_{0}=0$, $x_{1}=x_{0}+h,$... $x_{n-1}$=$x_{n-2}+h, x_{n}=b.$

Consider y=f(x) Now find the value of $y$($y_{0}$ to $y_{n}$) for the corresponding $x$($x_{0}$ to $x_{n}$) values.

Now, substitute all the values in the Simpson's one third rule.

The formula for Simpson's one third rule is :

$\int_{x_{0}}^{x_{0}+n h} f(x) d x=\frac{h}{3}[(y_{0} +y_{n})4(y_{1} +y_{3}+.....+y_{n-1} )+2(y_{2}+y_{4}+...+y_{n-2})]$

To apply Simpson's one-third rule, the number of intervals must be a multiple of two.

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