# Double integral of a surface

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Andromeda on 11 Nov 2021
Commented: Andromeda on 11 Nov 2021
The correct answer of the double integral of the surface sqrt(x)-y^2 is 1/7 but the program output is 301/1430. Where have I gonne wrong? See code below
syms x y
format rational
Function = @(x,y) x.^(1/2)-y.^2;
xmin = @(y) y.^4;
xmax = @(y) y.^(1/2);
Double_integral = integral2(Function,0,1,xmin,xmax);
disp(Double_integral)
Andromeda on 11 Nov 2021
Sure
my functon was supposed to be in the form of @(y,x). @Walter Roberson pointed that out

Walter Roberson on 11 Nov 2021
xmin - real number
xmax - real number
ymin - real number | file handle
ymin - real number | file handle
Notice that your function handles are named xmin and xmax suggesting that they are limits on x rather than limits on y. But integral2() requires that the x limits be placed before the y limits, and does not permit function handles for the x limits.
What is the solution? This: exchange your x and y in your function.
format rational
Function = @(y,x) x.^(1/2)-y.^2;
xmin = @(y) y.^4;
xmax = @(y) y.^(1/2);
Double_integral = integral2(Function,0,1,xmin,xmax);
disp(Double_integral)
1/7
Andromeda on 11 Nov 2021
Hahaha, yes!! Thank you.