- #1
SNOOTCHIEBOOCHEE
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Homework Statement
Let E = [0, 1] × [0, 1] be a Jordan region and f : E --> R be defined as
f(x, y) = x + y.
By using the definition 12.17, show that f is integrable on [0, 1]×[0, 1]. I.e., form proper
grids to prove the integrability.
Homework Equations
Definition 12.17 (i shortened it):
F is integrable on E if for all epsilon >0 there exists a grid G such that
U(f,g)- L(f,g)< epsilon
(U(f,g) is the upper sum)
The Attempt at a Solution
Ok i honestly don't know how to define a grid G.
This seems like a really simple question unless there is something i am not getting, i figure the best way to approach this problem is just to come straight out and define a grid g.
Edit: wait. i think that the sup will always be 1 over this entire region, which means that U(f,g) <1 ... but i don't know where to go from there,