Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

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 change-of-variables 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=x-y. |J(x,y)|=|∂(u,v)/∂(x,y)|=1-(-1)=2; dudv=2dydx ∬dydx = ∬1/|J(x,y)| dudv = ∬0.5 dudv Thank you

OCW Scholar - Multivariable Calculus
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Join Brainly to access

this expert answer

SIGN UP FOR FREE
  • phi
I think dA= dx dy and they are saying \[ \int \int du\ dv = \int \int | J(x,y) |\ dx\ dy \]
Oh, it makes perfect sense to me now. Thank you very much!

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Not the answer you are looking for?

Search for more explanations.

Ask your own question