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Answer by Sebastiano for Do double integrals always give a volume?
The topic of double integrals$$\iint_D f(x,y) \ dxdy$$affirms that from the geometric point of view it can be interpreted as the volume of the solid obtained by extending the plane region $D$ until the...
View ArticleAnswer by Toby Bartels for Do double integrals always give a volume?
If you think of an ordinary integral $ \int _ a ^ b g ( x ) \, \mathrm d x $ as an area (or a signed area in case $ g $ might take negative values), then you can think of a double integral $ \int _ R f...
View ArticleDo double integrals always give a volume?
I'm trying to figure out more concretely what double integrals give.Say:$$\iint f(x,y) \ dA $$Essentially, what is happening, is the integration of a function over an area? If we break it down integral...
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