# Get help with Simpson's rule questions

Recent questions in Simpson's Rule

### 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 Answered

### Calculate:${\int }_{-14}^{-8}ydx$

Alannah Short 2022-06-14 Answered

### 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 Answered

### 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 Answered

### Approximate ${\int }_{0}^{1}\phantom{\rule{mediummathspace}{0ex}}\sqrt{2-{x}^{2}}dx$ using the trapezoidal and simpson's rule for $4$ intervals.Now we can determine the simpson rule is$\frac{h}{3}\left(f\left({x}_{0}\right)+4f\left({x}_{1}\right)+2f\left({x}_{2}\right)+4f\left({x}_{3}\right)+f\left({x}_{4}\right)\right)$and the trapezoidal rule is$\frac{h}{2}\left(f\left({x}_{0}\right)+2f\left({x}_{1}\right)+2f\left({x}_{2}\right)+2f\left({x}_{3}\right)+f\left({x}_{4}\right)\right)$and $h=\frac{b-a}{n}$ which I assume is $\frac{1-0}{4}$but how we add it all together?

Imani Bentley 2022-06-01 Answered

### Does that make the answer from the Definite Integration a $100$ accurate? or is it just a more accurate estimation?

Wayne Steele 2022-05-23 Answered

2022-05-17

### How to derive the quadrature weights for the trapezoid and the Simpsons rule?Trapeziod rule:$\underset{a}{\overset{b}{\int }}f\left(x\right)$$\approx$$\frac{b-a}{2}$$\left[f\left(a\right)+f\left(b\right)\right]$Simpson's rule:$\underset{a}{\overset{b}{\int }}f\left(x\right)$$\approx$$\frac{b-a}{6}$$\left[f\left(a\right)+4f\left(\left(a+b\right)/2\right)+f\left(b\right)\right]$

Aedan Gonzales 2022-05-10 Answered

### The function,$f\left(x\right)={e}^{x}$at $11$ equidistant points on the interval $\left[0,1\right]$.The question asks whether the trapezoidal rule on $10$ subintervals would give a better approximation than the Simpson rule on $10$ subintervals on the provided function?

Laila Andrews 2022-05-10 Answered