(See Solution) Use the idea of volume calculation to explain the statement: If for a given function f(x, y) takes only positive values on a given region
Question: Use the idea of volume calculation to explain the statement:
If for a given function \(\mathrm{f}(\mathrm{x}, \mathrm{y})\) takes only positive values on a given region \(R\) in the x y -plane, then
\[\iint_{R} f(x, y) d x d y>0\]
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![[Solution] Explain the statement: If for a](/images/solutions/MC-solution-library-37614.jpg "[Solution] Explain the statement: If for a given function f(x,")
[Solution] Explain the statement: If for a given function f(x,
![[All Steps] The region R is plotted](/images/solutions/MC-solution-library-37615.jpg "[All Steps] The region R is plotted in the xy-plane y(y-6)+1,")
[All Steps] The region R is plotted in the xy-plane y(y-6)+1,
![[See Steps] Consider the region R plotted](/images/solutions/MC-solution-library-37616.jpg "[See Steps] Consider the region R plotted in the xy plane x(t)=")
[See Steps] Consider the region R plotted in the xy plane x(t)=
(Solution Library) Consider the region R plotted in the xy plane Where
![[Steps Shown] Here is another region R](/images/solutions/MC-solution-library-37618.jpg "[Steps Shown] Here is another region R plotted in the x y -plane 3")
[Steps Shown] Here is another region R plotted in the x y -plane 3
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