average value of a double integral over a region

lundi 28 juillet 2014

1. The problem statement, all variables and given/known data

f(x,y) = ##e^{x+y}## D is the triangle vertices (0,0), (0,1) , (1,0)







2. Relevant equations



##f(x,y)_{avg}=\frac{\iint_D f(x,y) dA}{\iint_D dA}##







3. The attempt at a solution



##\iint_D dA \Rightarrow \int_{0}^{1}\int_{0}^{-y+1} dxdy = \frac{1}{2}##



##\iint_D f(x,y) dA \Rightarrow \int_{0}^{1}\int_{0}^{-y+1} e^{x+y}dxdy ##



##\int_{0}^{1} e - e^y dy = 1##





##f(x,y)_{avg} = \frac{1}{1/2} = 2##



this doesn't seem correct.





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