# Simpsons Rule: With for loops

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Eric on 10 May 2015
Answered: Malek Arnous on 20 Dec 2017
Hi, So I have a question where I have to use Simpsons rule to integrate (1-x^3)*sin(x) + exp(x^2/20) between -1 and 4 with 20 intervals. The function has 4 inputs, f(x), a,b (start and end points) and n intervals
I know that I can make this code simpler with the sum function but unfortunately I have to use loops for this exercise.
My code looks like this:
function integral = simpsonsrule(f,a,b,n)
h = (b-a)/n;
x = linspace(a,b,n);
x4=0;
x2=0;
for j=2:2:b
x4 = x4 + f(x4);
end
for k=3:2:b
x2= x2 + f(x2);
end
integral = (h/3)*(f(a)+ f(b) + 4*(x4)+ 2*(x2));
end
And I'm calling it like this:
clear;
integral = simpsonsrule((1-x.^3)*sin(x) + exp(x.^2/20),-1,4,20)
But I'm getting the error: Undefined function or variable 'x'. but haven't I defined it with x=linspace(a,b,n)?

Walter Roberson on 10 May 2015
integral = simpsonsrule(@(x) (1-x.^3)*sin(x) + exp(x.^2/20),-1,4,20)
You need the @(x) to make an anonymous function
Eric on 10 May 2015
I've been using 20,50,100,500,1000.

Malek Arnous on 20 Dec 2017
yes