Solving Integrations with Simpson's Rule
1 view (last 30 days)
Show older comments
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/904840/image.png)
MY CODE:
syms r
r0 = 3; % Radius of the pipe in cm
% Given equation: Q = integration of v*dA
% Cross sectional Area, A = pi*r^2
% dA = 2*pi*r*dr
% v = 2*(1-(r/r0))^(1/6)
% Declare the function
Q = 4*pi*r*(1-r/r0)^(1/6);
n = 1280; % Number of segments
a = 0; % Lower limit in min
b = 3; % Upper limit in min
simp_int = simpson(Q, n, a, b)
function integral = simpson(func, n, a, b)
h = (b-a)/n;
x = a;
sum = feval(func,x);
for i = 1:2:n-2
x = x+h;
sum = sum+4*feval(func,x);
x = x+h;
sum = sum+2*feval(func,x);
end
x = x+h;
sum = sum+4*feval(func,x);
sum = sum+feval(func,b);
integral = (b-a)*sum/(3*n);
end
MY CODE ERROR:
Error using feval
Function to evaluate must be represented as a string scalar, character vector, or function_handle object.
Error in untitled>simpson (line 23)
sum = feval(func,x);
Error in untitled (line 19)
simp_int = simpson(Q, n, a, b)
0 Comments
Answers (2)
David Hill
on 23 Feb 2022
Edited: David Hill
on 23 Feb 2022
You are doing numerical integral, no reason for symbolics.
r0 = 3;
f=@(r)4*pi*r.*(1-(r/r0)).^(1/6);
n = 1280;
a = 0;
b = 3;
h = (b-a)/n;
x = a;
s=f(x);
for i = 1:2:n-2
x = x+h;
s = s+4*f(x);
x = x+h;
s = s+2*f(x);
end
x = x+h;
s = s+4*f(x);
s = s+f(b);
Integral = (b-a)*s/(3*n);
%Using built-in MATLAB functions
Integral2=integral(f,0,3);
r=0:.00001:3;
Integral3=.00001*trapz(f(r));
0 Comments
AndresVar
on 23 Feb 2022
Edited: AndresVar
on 23 Feb 2022
You need to declare Q as a function handle or use subs.
syms r
r0=3;
Q = 4*pi*r*(1-r/r0)^(1/6);
subs(Q,'r',0)
%%% Alternatively declare Q(r)
clear;
syms Q(r)
r0=3;
Q(r)=4*pi*r*(1-r/r0)^(1/6);
Q(0)
%%% feval declare Q as anonymous function
clear;
r0=3;
Q=@(r) 4*pi*r*(1-r/r0)^(1/6);
feval(Q,0)
0 Comments
See Also
Categories
Find more on Calculus in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!