 # Simpson's Rule Examples and Equations: Master the Concepts with Our Expert Help

Recent questions in Simpson's Rule Julian Clements 2023-01-30

## A= {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} write the sets using rule method bandikizaui 2022-07-15

## Which rule for numerical integration is more accurate, the Trapezoidal Rule or the Simpson Rule? letumsnemesislh 2022-07-10

## The trapezoidal rule applied on ${\int }_{0}^{2}\left[f\left(x\right)\right]dx$ gives the value 5 and the Midpoint rule gives the value $4$. What value does Simpson's rule give? Wisniewool 2022-07-05

## Use both trapezoid and Simpson's rule to find ${\int }_{0}^{\mathrm{\infty }}{e}^{-x}dx$ starting with $h=2$ where $h$ is the length of subintervals $\left[{x}_{i},{x}_{i+1}\right]$. Waldronjw 2022-07-03

## Problem applying Simpson's rule$I={\int }_{0}^{2}\frac{1}{x+4}dx$with $n=4$. Esmeralda Lane 2022-07-02

## What difference Between Simpsons Rule and $3/8$ rule? Lorena Beard 2022-07-01

## Given the following data on $y=f\left(x\right)$,$\overline{)\begin{array}{cc}\text{x}& \text{y}\\ 0& 32\\ 1& 38\\ 2& 29\\ 3& 33\\ 4& 42\\ 5& 44\\ 6& 38\end{array}}$Calculate approximately ${\int }_{0}^{6}f\left(x\right)dx$. abbracciopj 2022-06-30

## Evaluate the following using Simpson's rule (by using 2 strips).${\int }_{1.6}^{1}\frac{sin2t}{t}dt$ Eden Solomon 2022-06-27

## Does there exist a monic ${x}^{n}$, $n>4$, for which Simpson’s rule is exact? If not, why?$S\left(f\right)=\frac{b-a}{6}f\left(a\right)+\frac{2\left(b-a\right)}{3}f\left(\frac{a+b}{2}\right)+\frac{b-a}{6}f\left(b\right)$ Sattelhofsk 2022-06-26

## Is there any mathematical proof that I can always get a accurate value using composite simpson's rule rather than only using $\frac{3}{8}$ simpson's rule? First of all is my claim correct that we yield a better accuracy always with composite simpson's rule? Semaj Christian 2022-06-26

## Derive Simpson's rule with error term by using${\int }_{{x}_{0}}^{{x}_{2}}f\left(x\right)\phantom{\rule{thinmathspace}{0ex}}dx={a}_{0}f\left({x}_{0}\right)+{a}_{1}f\left({x}_{1}\right)+{a}_{2}f\left({x}_{2}\right)+k{f}^{\left(4\right)}\left(\xi \right)$Find ${a}_{0}$, ${a}_{1}$, and ${a}_{2}$ from the fact that Simpson's rule is exact for ${x}^{n}$ when $n=1$, $2$, and $3$. Then find k by applying the integration formula with $f\left(x\right)={x}^{4}$.We certainly get the correct coefficients, but I don't see how this tells us we can combine ${\xi }_{1}$ and ${\xi }_{2}$ xonycutieoxl1 2022-06-21

## I've got two equal length vectors $x,y$ representing the pairs $\left({x}_{i},f\left({x}_{i}\right)\right)$ and the components of the $x$ array aren't equally spaced.Is there some modified version of Simpson's Rule that fits my purposes ? telegrafyx 2022-06-21

## Relation between Simpson's Rule, Trapezoid Rule and Midpoint Rule. How $2n$ numbers come out at the left side while only $n$ numbers at the right side. migongoniwt 2022-06-18

## Prove that the simple Simpson’s rule${\int }_{a}^{b}f\left(x\right)dx\approx \frac{\left(b-a\right)}{6}\left[f\left(a\right)+4f\left(\frac{a+b}{2}\right)+f\left(b\right)\right]$is exact for all cubic polynomials. Dale Tate 2022-06-15

## Calculate:${\int }_{-14}^{-8}ydx$ Alannah Short 2022-06-14

## The error bound formulas for trapezoidal rule and simpson's rule say that:Error Bound for the Trapezoid Rule: Suppose that Using these formulas, is it possible to find functions where Trapezoid Rule is more accurate than Simpson's rule? Ezekiel Yoder 2022-06-13

## Prove: Let$S\left(n\right)$ and $T\left(n\right)$ be the approximations of a function using n intervals by using Simpson's rule and the Trapezoid rule respectfully.$S\left(2n\right)=\frac{4T\left(2n\right)-T\left(n\right)}{3}$ boloman0z 2022-06-13

## From a proof of Simpson's rule using Taylor polynomial where $f\in \left[{x}_{0},{x}_{2}\right]$ and, for${x}_{1}={x}_{0}+h$where$h=\frac{{x}_{2}-{x}_{0}}{2}$it got:${\int }_{{x}_{0}}^{{x}_{2}}f\left(x\right)dx\cong 2hf\left({x}_{1}\right)+{h}^{3}\frac{{f}^{″}\left({x}_{1}\right)}{3}+{h}^{5}\frac{{f}^{\left(4\right)}\left(\xi \right)}{60}$and then, it changed ${f}^{″}\left({x}_{1}\right)$ by$\frac{f\left({x}_{0}\right)-2f\left({x}_{1}\right)+f\left({x}_{2}\right)}{{h}^{2}}$Where it came? Jasmin Pineda 2022-06-12
## $\frac{\left(b-a{\right)}^{5}{f}^{\left(4\right)}\left(c\right)}{2880{n}^{4}}$for a $c\in \left[a,b\right]$, if the function has a continuous fourth derivative.Is this for any $c$ in the interval, or just a unique one? Tananiajtac2 2022-06-03