Calculating integration limits of a double integral

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mj702 2020-11-24

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编辑： Rohit Pappu 2020-11-30

Hello,

I am working on a college assignment to calculate the symbolical value and the numerical approximation of the double integral of

over the region defined by

and to determine the integration limits in y by symbolical computation.

Unfortunately, I haven't been able to figure out how to calculate the integration limits without knowing the final result. Sorry if this is easy, but I am a beginner in Matlab and my knowledge of double integrals isn't very profound.

Could someone please give me a hint how to solve this problem?

Thank You.

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Bruno Luong 2020-11-27

编辑：Bruno Luong 2020-11-27

x^2/6 + y^2/4 = 1 is a curve (ellipse). It's 1D manifold. I don't know hat "double integral" is doing here. You probably want a curviline integral.

Bruno Luong 2020-11-27

在 MATLAB Online 中打开

The integral is 0 since the function is odd in x

f(x,y)=-f(-x,y)

and the domain is symetric in x.

(x,y) in domain then (-x,y) is in.

You can deduce the same conclusion with y variable.

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回答（1 个）

Rohit Pappu 2020-11-27

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https://ww2.mathworks.cn/matlabcentral/answers/659988-calculating-integration-limits-of-a-double-integral#answer_557443

编辑：Rohit Pappu 2020-11-30

在 MATLAB Online 中打开

For computing the numerical approximation of the above double integral

%% Define the major and minor axis of ellipse
a = sqrt(6);
b = sqrt(4);
%% Define f(x,y)
fun = @(x,y) sin(x.*y);
%% Convert f(x,y) into f(r,theta) 
polarfun = @(theta,r) fun(a*r.*cos(theta), b*r.*sin(theta))*a*b.*r;
%% x = a*r.*cos(theta), y = b*r.*cos(theta) , dxdy = a*b*r*dr(dtheta)
%% Assign upper limit for r
rmax =1;
%% Calculate the integral for r = [0,1] and theta = [0,2*pi]
q = integral2(polarfun,0,2*pi,0,rmax)