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

quekyuxuan
 9 months 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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