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Question: Integration over an implicit domain

Question:Integration over an implicit domain

Jean-Claude Arbaut 142 Maple
integration
December 27 2020
2

Is there a way to tell Maple to compute an integral over a domain defined by an implicit condition?

A trivial example would be: integrate 1 over the 2D domain defined by x^2+y^2<=1.

I know it's possible to write the explicit double integral

int(int(1,y=-sqrt(1-x^2)..sqrt(1-x^2)),x=-1..1);

Or even as a single integral:

integrate(2*sqrt(1-x^2),x=-1..1);

However, it's not always possible to do this explicitly, depending on the form of the relation f(x,y)=0 defining the domain.

 

My idea was:

int(Heaviside(1-x^2-y^2),[x=-1..1,y=-1..1]);

But Maple returns 0. However, evalf/Int returns the correct numerical value of Pi.

 
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