double integration with loop

Question

José Anchieta de Jesus Filho 2020-3-6

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/509422-double-integration-with-loop

评论： José Anchieta de Jesus Filho 2020-3-7

采纳的回答： darova

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thank you very much if anyone can help me.

so, I need to create a loop that calculates integrals at each point. Say I have the following function handle

D = @(x,y) x.*(Z(x,y).^2);

from that function, I need to calculate a double integral and create the following loop

int1 = @(y) integral(@(x)D(x,y),x1,x2,'ArrayValued',true);
int2 = integral(@(y)int1,y1,y2,'ArrayValued',true);
c1 = int2./g % g is a scalar number
int11 = @(y) integral(@(x)D(x,y),x2,x3,'ArrayValued',true);
int22 = integral(@(y)int11,y1,y2,'ArrayValued',true);
c11 = int22./g % g is a scalar number
int111 = @(y) integral(@(x)D(x,y),x3,x4,'ArrayValued',true);
int222 = integral(@(y)int111,y1,y2,'ArrayValued',true);
c111 = int222./g % g is a scalar number
.
.
.

i'm trying to do like this

x = 1:0.1:5
for i = 1:length(x)
    D = @(x,y) x.*(Z(x,y).^2);
    int1(i) = @(y) integral(@(x)D(x,y),x(i),x(i)+0.5,'ArrayValued',true);
    int2(i) = integral(@(y)int1(i),y1,y2,'ArrayValued',true);
    c = int2(i)./g
end

I need to plot a graph of c versus x

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Walter Roberson 2020-3-6

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p1 = @(r) integral(@(z1) dF(z1,r),z0,z0+e,'ArrayValued',true); % e is also a scalar

p1 is a function handle.

F = integral(@(r) p1,ri,re,'ArrayValued',true);

@( r) p1 is a handle to an anonymous function that accepts a single parameter and ignores the parameter and returns the function handle p1. You should be just using

F = integral(p1,ri,re,'ArrayValued',true);

José Anchieta de Jesus Filho 2020-3-6

thank you very much, I will modify. But, you know how to change the function to calculate the integral for various values of z0

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Answer 1

darova 2020-3-6

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/509422-double-integration-with-loop#answer_418949

在 MATLAB Online 中打开

Here is a shot

z0 = 0:0.001:0.03;
c = z0*0;
Brt = @(z1,r) z1+r;
e = 0.1;
ri = 0;
re = 1;
ro = 15;
v = 2;
dF = @(z1,r) 2.*pi.*v.*ro.*(Brt(z1,r).^2).*r; % v , ro are scalar numbers
for i = 1:length(z0);
    F = integral2(dF,z0(i),z0(i)+e,ri,re);
    c(i) = F./v;
end
plot(z0,c)

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darova 2020-3-6

Please attach the whole code

José Anchieta de Jesus Filho 2020-3-7

在 MATLAB Online 中打开

I thank you so much for your help. I changed the code a little and managed to make it work. Thank you

for i = 1:length(z0)
    P = @(r) integral(@(z1) dF(z1,r),z0(i),z0(i)+e,'ArrayValued',true);
    F = integral(P,ri,re,'ArrayValued',true);
    c(i) = F./v;
end
plot(z0,c)