Question

Simpson's rule question

Answer 1

So I have \[\int\limits_{0}^{2}(x^3+3x^2)\]
and i found that the exact value is 12 using FTC
now it says to approxiamte with SIMP(n) when n=2 , n=4, and n=100.
i did the first two but is there an relatively quick way to find SIMP(100)????

Answer 2

@aaronq @abb0t your input is welcomed

Answer 3

also SIMP(2)=11.333
SIMP(4)=12.3343

Answer 4

For simpsons rule, I think you need to find the width of the points ∆x = \(\sf \color{}{\frac{b-a}{n}}\)
I am not going to do the arithmetic for you, because I am sure that it's in your book, but you should get: \[\int\limits_{a}^{b}f(x) dx \approx \frac{\Delta x}{3} [f(x_0)+4f(x_1)+2f(x_2)+...+2f(x_{n-2})+4f(x_{n-1})+f(x_n)]\]

Answer 5

Focus on the relation, which is that the function evaluations at points with odd subscripts are multiplied by 4 and all the function evaluations at points with even subscripts (except for the first and last) are multiplied by 2.

Answer 6

As far as using n = 100, you could use MATLAB. If you have the program on your computer or campus computer.