# Questions tagged [simpsons-rule]

For questions regarding Simpson's rule and its applications.

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Implementing on Matlab the Simpson adaptive rule to approximate an integral (the following code), I am struggling with saving nodes correctly. I have tried different solutions, but none of them seems ...
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### Simpson's 3/8 method [closed]

What are the advantages and disadvantages of simpson's $\frac {3}{8}$ rule. Also what are the applications of this rule.
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### How to choose interval count for simpsons rule?

Is there some ways to compute interval count for [a; b] according to some error $\epsilon$? Or maybe according to function properties and interval size?
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### Simpsons rule and follow up question to expressing the integral of a function as $\pi$

Use Simpsons rule with n = 4 to estimate the integral $\int_0^2\sqrt{4-x^2}dx$. Notice that the integral gives you an approximation for ${\pi}$ and therefore demonstrate without evaluating this ...
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### Modified simpson's rule for varying step sizes

I'm reading the paper A Modified Simpson's Rule and Fortran Subroutine for Cumulative Numerical Integration of a Function Defined by Data Points by L.V. Blake, and it notes, on page 8 a further ...
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### Implementation of cumulative simpson method

I am working on a program which uses cumulative integration methods to solve differential equations, and I want to confirm that my implementation of the Simpson method is correct, as I could not find ...
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### Richardson extrapolation Simpson's rule

"Assume that S(h) is equivalent to the (composite) Simpson's rule where h is the size of the step. Correct use of Richardson's extrapolation gives the formula: $R(h) = \frac {16S(h)-S(a)} {b}$. What's ...
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### Use Simpson's rule to estimate the error of integral $\int_1^5 \ln(x) \mathrm dx$

In my homework I'm requested to estimate the error of the definite integral: $$\int_1^5 \ln(x) \mathrm dx$$ I am also given the formula: $$|E_n|<= \frac {(K(b-a)^5)}{180N^4}$$ Where K is an ...
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### How to approximate the following improper integral by using Simpson's rule

I am trying to approximate the following integral by using Simpson's Rule with $n=6$ $$I = \int_{1}^{\infty} \frac{\sin(x)}{x^4} dx$$ The textbook I am using for Numerical Analysis (Burden, Faires 9-...
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