For questions regarding Simpson's rule and its applications.

learn more… | top users | synonyms

1
vote
1answer
92 views

How large should n be to guarantee that the Simpson's Rule approximation on the Integral (from 0 to 1) 19e^x^2 dx is accurate to within 0.0001?

I'm very lost on the following problem and will appreciate your help very much. How large should n be to guarantee that the Simpson's Rule approximation on the Integral (from 0 to 1) 19e^x^2 dx is ...
1
vote
2answers
46 views

internal rectangle area intersected by a circle

I need to compute the internal rectangle area intersected by a circle like (the blue area) on these 3 examples: I know every vertex (x,y) coordinate and then their distance from circle center but ...
0
votes
1answer
66 views

Help me integrate this function using Simpson's rule

I have a question: compute $$\int_0^1 \frac{\sin(x)}{x}\,dx$$ for $n=10$ divisions. I got the value $0.9127$ but I think its a bit too high.
0
votes
1answer
20 views

Newton-cotes formulas help

I am having a hard time understanding how to use this formula. If given the following problem: Compute ∫ sin x dx using Simpson's rule with 3 points in the range 0 to Pi/2. Do I have to take the ...
1
vote
0answers
49 views

Simpson's rule error rate for N-dimension

I'm doing a project that involves numerical method, but I'm not too familiar on calculus. I'm using Simpson's rule to integrate n-dimension gaussian, I was able to get the integration result for ...
0
votes
0answers
59 views

Local truncation error

(a) Find the local truncation error for the Trapezoidal rule $$ Y_{n+1} -Y_n= h/2( F_{n+1} + 3F_n)$$ and hence find the order of the method. What do you expect would happen to the local errors ...
0
votes
1answer
394 views

Do I have the right formula for the Composite Simpson's 3/8 Rule?

Let $n$ be the number of segments, which is a multiple of 3. And let $h$ be the width of each of these segments, where $h=\dfrac{(b-a)}{n}$. So the formula I have is that the integral $I$ for a ...
0
votes
1answer
103 views

Doubling Number of Nodes In Composite Simpson's Rule

Let n be even. Show how the composite Simpson rule with 2n equally spaced nodes can be computed from the case of n equally spaced nodes with a minimum amount of additional work. I've been working on ...
1
vote
1answer
18 views

How do I get an answer of $14$ using simpsons rule for $\frac{152e}{180n^4}<.0001$

I must have the algebra wrong somewhere but here is the original equation: $$\frac{152e}{180n^4}<.0001$$ If I then multiply like this: $$152e<.0001(180)n^4$$ Which then gives: $$152e < ...
0
votes
1answer
192 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 ...
0
votes
2answers
722 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 ...
0
votes
0answers
117 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 ...
0
votes
1answer
58 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 ...
2
votes
1answer
138 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 ...
2
votes
1answer
139 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 ...
1
vote
1answer
1k 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 ...
0
votes
0answers
146 views

Generating parabola from points applet

Does anyone know of an applet or something that generates a parabola (graph and/or equation) given three (unique, non-colinear) points? I'm going to be mentioning this fact to my students as an aside ...
0
votes
1answer
105 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 ...