A community for students.
Here's the question you clicked on:
 0 viewing
quekyuxuan
 11 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
 11 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

This Question is Closed

phi
 11 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
 11 months ago
Best ResponseYou've already chosen the best response.0Oh, it makes perfect sense to me now. Thank you very much!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.