What does the integrand in a double integral represent? I see this problem and I'm not sure what the integrand here represents. Can someone tell me what it visually represents here?
Let $$S=\iint f(x,y)dxdy$$
When $ f(x,y)=1 $, $ S $ is a surface.
When $ f(x,y)\ne 1 $, $ S $ is a volume and $ f(x,y)dxdy $ is the elementary volume with $ dxdy$ as a base surface and $ f(x,y)$ as its height.
Let $$S=\iint f(x,y)dxdy$$
When $ f(x,y)=1 $, $ S $ is a surface.
When $ f(x,y)\ne 1 $, $ S $ is a volume and $ f(x,y)dxdy $ is the elementary volume with $ dxdy$ as a base surface and $ f(x,y)$ as its height.