Trapezoid Rule method errors

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Coolman
Coolman 2021-3-14
回答： Uday Pradhan 2021-3-19
I am trying to do a similar thing to my other question but using trapz command instead. can someone explain what I have done wrong.
function Trapezoid_Rule(~,~)
uavg = input('average velocity m/s ');
R= input('inner radius m ');
syms x r
T = uavg.*pi.*R.^2;
B = (1-(r./R).^2).*r;
BI = trapz(x,trapz(r,B,2));
disp(BI)%print the values in the command promt
end
Error using trapz (line 47)
Dimension argument must be a positive integer scalar within indexing range.
Error in coursework>Trapezoid_Rule (line 131)
BI = trapz(x,trapz(r,B,2));
Error while evaluating UIControl Callback.
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darova
darova 2021-3-14
r = linspace(0,R,100);
x = linspace(0,2*pi,100);
Coolman
Coolman 2021-3-14
Error using trapz (line 47)
Dimension argument must be a positive integer scalar within indexing range.
Error in coursework>Trapezoid_Rule (line 132)
BI = trapz(x,trapz(r,B,2));
Error while evaluating UIControl Callback.
gets to B even generating a series of numbers and then BI crashes with above error

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回答（1 个）

Uday Pradhan
Uday Pradhan 2021-3-19
Hi,
The error you have posted occurs because the integral:
trapz(r,B,2)
evaluates to 0. This is then used as the dimension argument while evaluating the exterior integral, hence the error.
The function "trapz" is to be used to numerically approximate the integral of a function over a certain interval.
With the help of the documentation, I have made some changes that lets you find the approximate inegral of B over the domain mentioned in your question. Hope it will help you!
uavg = input('average velocity m/s ');
R= input('inner radius m ');
%syms x r
r = 0:0.1:R;
theta = 0:0.1:(2*pi);
[R1,Theta] = meshgrid(r,theta);
T = uavg.*pi.*R.^2;
B = (1-(R1./R).^2).*R1;
%BI = trapz(x,trapz(r,B,2));
BI = trapz(theta,trapz(r,B,2));

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