# Questions tagged [simpsons-rule]

For questions regarding Simpson's rule and its applications.

101 questions
1answer
14 views

1answer
38 views

### Am I using the Simpsons rule and Gauss-Legendre method correctly? [closed]

I have the integral here: Simpsons rule: Answer 414.11411 Gauss-Legendre method Here the limits are x+y I found the answer to be around 0.923 Just wanted to make sure these values are correct.
2answers
45 views

### Numerical Integration Bounded by Two Singularities

I would like to solve the following definite integral numerically using Simpson's Rule, however it has singularities at both ends. I was told it's possible to perform a simple change of variable in ...
1answer
62 views

### How do I calculate $\int_1^3$ $x \ln (x)\ dx$ with a given accuracy, using Simpson's rule?

How do I calculate $\int_1^3 x \ln (x)\ dx$ with a given accuracy, in this case $10^{-4}$ using Simpson's rule? The problem I encounter is that the fourth derivative is $=2/x^3$. So how do I go ...
1answer
47 views

### Simpson's Rule over [-3,3]

To Find $I = \int_{-3}^3 \sin x^4 dx$ using the Simpson's (Parabolic) rule with $n=6$ intervals. $h=\frac{b-a}{n}=\frac{3-(-3)}{6}=1$ \begin{array}{|c|c|c|}\hline x\rightarrow&x_0&x_1&...
0answers
97 views

### Simpson vs. trapezoidal rule for numerically integrating $\cos{x}\cosh{x}$ in range 0 to $\pi$?

I have to numerically calculate many integrals similar to this: $$\int_0^\pi \cosh{\left(\frac{a_1\cos{x}+a_2\cos{2x}+a_3\cos{3x}+\ldots}{10}\right)}\cos{jx}\cos{kx}\space dx$$ Right now I am using ...
0answers
33 views

### Integrating using Simpson's Rule

Suppose there are functions $$g(x) = \frac{(2 \cdot \lfloor x\rfloor)}{(3\cdot x - \lfloor x \rfloor)} \tag{1}$$ and $$f(x) =\frac{\mid g(x)\mid}{ g(x)} \tag{2}$$ Now how do we do the definite ...
2answers
305 views

### What is the order of the midpoint rule?

If the Trapezoidal-Rule has the order $n=1$, and Simpson's has order $n=2$, what is the order $n$ of the midpoint rule? And if the weights of the Trapeziumrule are ($1/2, 1/2$) and those of the ...
1answer
133 views

1answer
88 views

### How large should $n$ be to guarantee that the Simpson's Rule approximation on $\int_0^1 9e^{x^2} dx$ is accurate to within $0.0001$?

Please help I am really struggling with this problem. I have been working on it and trying to look up how to do it but nothing is making sense. Thank you!
1answer
59 views

### Approximate derivative in midpoint rule error with notation of Big O

Error of midpoint rule is $E_m = \frac{f''(c)}{24}(b-a)^3$, where $c\in (a, b)$. I made research and I found out that i can approximate it by $E_m = \frac{f''(a)}{24}(b-a)^3 + O((b-a)^4)$, but i don'...
0answers
37 views

1answer
131 views

### Simson's Rule but Intervals Aren't the Same

I'm currently working on some homework, and ran into a question that has stumped me. We're working on Simpson's rule, which is easy enough, but then I got to a problem where the intervals aren't the ...
2answers
35 views

### Error in the simpson estimate

We can't find integrals of some fumulas like $sinx^2$, but we can get a approximate value using methods like the simpson method. Since only one order-two equation exits which passes 3 points, we ...
1answer
1k views

### Simpson's Rule derived from Lagrange Interpolation. Confused, please help.

I'm reading my lecturer's notes on how to derive the Simpson's Rule using Lagrange's Interpolating Polynomial, but there's a point that doesn't quite seem right. Here's a screenshot of the notes ...
1answer
93 views

1answer
2k views

### Why trapezoidal rule is giving better answers for some functions than Simpson's 1/3 rule? [duplicate]

Use appropriate quadrature formulae out of the trapezoidal and Simpson's rules to numerically integrate $\int_0^1\frac{dx}{1+x^2}$ with $h=0.2$. Hence obtain an approximate value of $\pi$. Justify the ...
1answer
975 views

### Find the arc length using Simpsons rule

I'm trying to find the arc length using Simpsons formula for this function: $\int_{0}^{\pi}\sqrt{1+cos^2(x)}$ where $h=\frac{\pi}{6}$ I've seen online that people solve this type of examples so that ...
1answer
5k views

2answers
353 views

### Is desmos plotting this fuction incorrectly?

I was just plotting a function in desmos: $f(x) = \frac{a}{b+x}$. I wanted to plot the integral, but desmos doesn't support indefinite integrals of functions, so to model the integral I used Simpsons ...
4answers
3k views

### Numerical Integration for integrable singularity

Till this time i have learned three numerical technique to find the definite integration. They are Simpson, Trapezoidal and Gauss-legendre formula. The sad thing is that I can't apply these theorem ...
0answers
236 views

### Simpson's rule with error $0$

I know that Simpson's rule is exact on all intervals for polynomials with $\deg(f) \leq 3$, but are these the only functions with the rule is exact for on all intervals? If so how would I prove this?
0answers
32 views

### How would you set up this integral to where you can perform Simpson's rule?

Not sure how to set up my deltax or even begin with this setting this problem up in general. Any help would be appreciated.
1answer
7k views

### Simpson rule for double integral

Compute a quadrature of $\int_c^d\int_a^b f(x,y)dxdy$ using the Simpson rule and estimate the error. So the Simpson rule says $S(f) = (b-a)/6(f(a)+4f((a+b)/2) +f(b))$ So i get \$\int_c^d(b-a)/...