calculating Double integral over a region

I am trying to plot this double integral but i keep getting an error, can someone help me out thanks.

ymax = @(x) sqrt((9-x.^2)/9);

ymin =@(x) -1.*sqrt((9-x.^2)/9);

fun = @(x,y) aa;

aaa =integral2(fun,-3,3,ymin,ymax);

aa = 2

Answer 1

[Torsten]

syms x y
int(int(2,y,-sqrt(1-(x/3)^2),sqrt(1-(x/3)^2)),x,-3,3)  

ans = 

[Carlos Guerrero García]

I think that Torsten answer is better than mine. I was trying to answer the question with minor changes in the original code, but Torsten code is easier and more elegant than mine. +1 to Torsten!!!

Answer 2

[Carlos Guerrero García]

When you define "fun", the variable "aa" is undefined yet. Also, because the variables "x" and "y" doesn't appear in the "fun" definition, the compiler provides another error. I suggest (avoiding the usage of the unnecesary declaration of the "aa" value) the following code, resulting the expected numerical value of 6*pi that is two times the area of an ellipse of semiaxes 3 and 1, as expected:

syms x y;
ymax = @(x)  sqrt((9-x.^2)/9);
ymin =@(x) -1.*sqrt((9-x.^2)/9); 
fun = @(x,y) 2+0*x+0*y; % Avoiding the "aa" declaration and incluing "x" and/or "y" in the function "fun"
aaa =integral2(fun,-3,3,ymin,ymax)

aaa = 18.8496