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anonymous
 one year ago
Hi all,
I'm looking at Part II of Problem Set 7, on Double Integrals. In the 4th paragraph of the background introduction to problems 4 and 5, it states
"The general changeofvariables formula says that if a region R goes to a region R' by a transformation (x,y) → (X,Y) with Jacobian ∂(X,Y)/￼∂(x,y), then the areas of R and R' are related by A(R') = ∬J(x,y) dA."
Shouldn't it be "A(R') = ∬1/J(x,y) dA" instead?
For example, let h=h(x,y); u=x+y; v=xy.
J(x,y)=∂(u,v)/￼∂(x,y)=1(1)=2; dudv=2dydx
∬dydx = ∬1/J(x,y) dudv = ∬0.5 dudv
Thank you
anonymous
 one year ago
Hi all, I'm looking at Part II of Problem Set 7, on Double Integrals. In the 4th paragraph of the background introduction to problems 4 and 5, it states "The general changeofvariables formula says that if a region R goes to a region R' by a transformation (x,y) → (X,Y) with Jacobian ∂(X,Y)/￼∂(x,y), then the areas of R and R' are related by A(R') = ∬J(x,y) dA." Shouldn't it be "A(R') = ∬1/J(x,y) dA" instead? For example, let h=h(x,y); u=x+y; v=xy. J(x,y)=∂(u,v)/￼∂(x,y)=1(1)=2; dudv=2dydx ∬dydx = ∬1/J(x,y) dudv = ∬0.5 dudv Thank you

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phi
 one year ago
Best ResponseYou've already chosen the best response.1I think dA= dx dy and they are saying \[ \int \int du\ dv = \int \int  J(x,y) \ dx\ dy \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh, it makes perfect sense to me now. Thank you very much!
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