# Tagged Questions

For questions regarding Simpson's rule and its applications.

26 views

### Rate of convergence for quadratures

How can I find the observed (practical) order of convergence of a quadrature? I remember the formula $\frac{|x_{n+1}-x_{n}|}{|x_{n}-x_{n-1}|^q}$ but does this work here aswell? This formula gives me ...
98 views

19 views

### Integral with Simpson's method not converging

I'm trying to use Simpson's rule to integrate the following function in a program: $$\int_{z_a}^{z_b}\frac{Cf(z)}{(C^2 - f(z)^2)^{3/2}}\,dz$$ where $C$ is a constant and $f(z)$ are interpolated ...
62 views

### A mathematical explanation of the Simpson's Paradox?

In general, Simpson's Paradox occurs because situation such as following occurs for some arbitrary events $A,B,$ and $C$: $P( A | B , C) < P(A| B^c,C)$ $P( A | B , C^c ) < P(A| B^c,C^c)$ But, ...
28 views

### Evaluating integral using Simpson's rule, error in book?

This is from Morris Kline's "An intuitive and Physical Approach" calc book, chapter 9 last section, page 264 problem 4. The problem states: Given the following data on a function $y = f(x)$: x: 0, ...
42 views

### Find an approximate value of R 2 1 x −2 dx using composite Simpson’s rule with h = 0.25. Giv

Find an approximate value of $\int _1^2 x^{-2} dx$ using composite Simpson's rule with h = 0.25. Give a bound on the error. Then calculate the exact value of the integration and compute the exact ...
59 views

### What value of $N$ to use in Simpson's rule to reach desired accuracy?

I need to calculate Simpsons rule for the integral of $$\frac{e^x-1}{\sin x}$$ from $0$ to $\pi/2$ with minimum number of intervals $N$ up to $10^{-6}$ accuracy. Wolfram alpha seems to be giving me a ...
134 views

### Simpson's Rule for IVP. Truncation Error proof

Edit: replaced all c's with y's as the c just denotes replacing a series of coupled linear equations Ay with uncoupled equations $\Lambda c$ no biggie. Im working through the lecture notes for a ...
162 views

### Confusion about order of accuracy of Simpson's rule

Suppose I have a function $f(x)$ which is to be integrated in the interval $[a,b]$ using step size $h$. Also, $b = a+2n\cdot h$ and $n \in \mathbb{N}$ I am unable to understand how exactly does the ...
69 views

### Simpson's rule with precision?

I have an integral: $$\int_0^1sinx^2dx$$ Task is to solve this integral using Simpson's rule with precision $\frac{1}{2}10^{-4}$. I am not sure how should I do that. I have this formula for ...
67 views

### Reasons for different answers when finding area using Simpsons rule and numerical integration? [closed]

I have a function $\sqrt{x^4(x+4)}$ to be integrated from 0 up to -4. Using Simpson's will give me 19.02 but using normal numerical methods giving me -19.5 ! What's the reason behind this difference ...
2k views

229 views

### Trapezoidal and simpson rule question here?

The trapezoidal rule applied on $\int_0^{2} [f(x)] dx$ gives the value 5 and the Midpoint rule gives the value 4. What value does Simpson's rule give? So we have that T=f(0)+f(2). The Simpson's ...
189 views

### Simpson's 3/8 Rule

When deriving Simpson's 1/3 Rule, I used a second order polynomial $P(x) = Ax^2 + Bx + C$, and integrated over the region $[-h,h]$ Integrating gave me: $\ \dfrac{h}{3}(2Ah^2 +6C)$ I evaluated $P(x)$...
753 views

### Find the approximate area using Simpson's Rule

Find the approximate area of the shaded figure shown using Simpson's rule. Each of the equidistant parallel chords is measured from the base to a point on the curve. All units are expressed in km. ...
81 views

### Find upper limit of normal distribution integration

Considering the normal distribution with standard deviation equals to 0.9 and mean 2.1: $$P(X\leq a) = \frac{1}{0.9\sqrt{2\pi}}\int_{-\infty}^{a} e^{-\frac12\frac{(x-2.1)^2}{0.9^2}}\,dx$$ I must ...
246 views

### Simpson's rule over cubic splines

I'm helping a friend of mine to do her homework, but i need help understanding some results (sorry but i took numeric methods class a looooong time ago) So, the task is to fit a cubic spline over ...
66 views

### Quadrature obtained from Simpson's rule, and its order of error

Express $Q$ as a weighted combination of the five function values $f(a)$ through $f(e)$ and establish that its order is six. (See section 6.2.) This is from Numerical Methods by Moler, http://www....
79 views

594 views

### Simpson's Error Bound Estimation

The problem: I need to use Error Bound to find n (least) to the $10^{-9}$ in approximating the integral of 5e^x^2 from 0 to 1 I'm using $$Error(Sn) \le \frac{k(b-a)^5}{180N^4}$$ I found the 4th ...
2k views

### Use Error Bound to Find Least Possible Value of N

I greatly appreciate it if someone could help me with this problem: Use the Error Bound to find the least possible value of $N$ for which $Error(S_N)\le 1 \times 10^{-9}$ in approximating the ...
157 views

### Compute multiple Rectangles area intersect by a circle

I've a need to compute the area of single elements (dice) of a matrix like this: http://i.stack.imgur.com/EKVSz.jpg The matrix is composed by 'c' columns and 'r' rows and every element/rectangle has ...
81 views

### Does Simpsons rule still apply when a < 0?

I am currently working on an assignment where I have to find the answer to the following integral using Simpsons rule:$\int x+1$ (MIN = -1 MAX = 3), I choose to have 6 intervals. I now start ...
219 views

### Error bound for $\cos(x^3)$ under Mn, Tn and Sn

In this problem we will approximate the integral of $\cos(x^3)$ over the interval $[0, 2]$. (a) Write an expression for MN, TN and SN with $N = 4$. (b) For each of the approximations determine an N so ...
230 views

### How to use undefined value in Composite Simpson's Rule

I have to use the Composite Simpson's Rule to approximate the integral $\int_0^1 t^2\cdot sin(\frac{1}{t}) dt$. I've used the Composite Simpson's Rule, but when I work through the algorithm, one step ...
3k views

### Length of bezier curve with Simpson's rule

I wish to approximate the length of a Bézier curve in a 2D plane. I could do this iteratively – and may – but I want to experiment using Simpson's rule. I am not sure how to set this up and could use ...
230 views

### numerical integration for N datapoints

I understand why Simpson's Rule is better than the trapezoidal rule for 3 datapoints (because under the assumption that the function is smooth, a parabolic approximation is going to be better than a ...