Calculus 3 Change of Variables: Jacobians

Click For Summary
The discussion focuses on evaluating the double integral of the function over a specified region defined by the curves y/x=1/2, y/x=2, xy=1, and xy=2. The participant is working on determining the change of variables functions in x and y, specifically using u=y/x and v=xy. They have successfully expressed y in terms of u and x but are encountering difficulties in solving the resulting equations. Guidance is requested to navigate the change of variables and complete the evaluation. The conversation emphasizes the importance of correctly applying the Jacobian in the transformation process.
Wargy
Messages
3
Reaction score
0

Homework Statement


Evaluate \int\inte^xy dA, where R is the region enclosed by the curves: y/x=1/2 , y/x=2, xy=1, and xy=2.


Homework Equations


None?


The Attempt at a Solution


I have the region graphed and I'm currently working on acquiring the change of variables functions in x and y. I have attempted to solve the system of equations with u=y/x and v=xy to obtain these but I'm having some trouble. If I could be pointed in the right direction I would be greatly appreciative! Thanks.
 
Physics news on Phys.org
You have u= y/x and v= xy so y= xu. Substitute that into v= xy: v= x2u. Now solve for x.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Find f(x,y) given partial derivative and initial condition
  • · Replies 6 ·
Replies
6
Views
2K
Change of variable for Jacobian: is there a method?
  • · Replies 5 ·
Replies
5
Views
2K
Calculate the joint CDF of two random variables
  • · Replies 2 ·
Replies
2
Views
2K
Calculus 3 change of variables
  • · Replies 3 ·
Replies
3
Views
1K
Determine limits of integration in double integral change of variables
  • · Replies 2 ·
Replies
2
Views
2K
Find the dimensions that will minimize the surface area of a Rectangle
  • · Replies 1 ·
Replies
1
Views
1K
Changing Variables and the Limits of Integration using the Jacobian
  • · Replies 21 ·
Replies
21
Views
2K
Find the local maxima and minima for##f(x,y) = x^3-xy-x+xy^3-y^4##
  • · Replies 5 ·
Replies
5
Views
1K
Double Integral via Appropriate Change of Variables
  • · Replies 3 ·
Replies
3
Views
2K
Problem solving this volume using Jacobi's Determinant
  • · Replies 1 ·
Replies
1
Views
2K