Calculus 3 change of variables

Click For Summary

Homework Help Overview

The discussion revolves around evaluating a double integral using a change of variables in a calculus context. The integral involves the expression (x + y) sin(x - y) over a specified region defined by several linear boundaries.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to visualize the region in both the xy and uv planes to determine the appropriate bounds for integration. There are concerns about the ability to accurately draw the necessary graphs to facilitate this understanding.

Discussion Status

Some participants express uncertainty about how to begin the problem, particularly in relation to graphing the boundaries. There is a recognition of the importance of visual representation in solving the problem, but no consensus on how to proceed has been reached.

Contextual Notes

Participants note difficulties with graphing the specified boundary lines, which may impact their ability to set up the integral correctly. There is an emphasis on the necessity of drawing these lines as part of the problem-solving process.

princessp
Messages
4
Reaction score
0

Homework Statement


Use the change of variables to evaluate the integral
(x +y ) sin(x -y )dA, where R is the
region enclosed by y = x, y = x - 2, y = -x and y = -x + 1. (Hint: use u = x + y and
v = x - y

Homework Equations

The Attempt at a Solution


Not sure how to start it
 
Physics news on Phys.org
Draw the region in the xy plane and then draw the region in the uv plane to determine bounds. From there, use the standard change of variables...
 
okay i think that's where i am having trouble. I an not good at drawing the graph
 
princessp said:
okay i think that's where i am having trouble. I an not good at drawing the graph

You have to draw the boundary lines. Don't say that you can not draw the lines y = x, y = x - 2, y = -x, and y = -x + 1 !
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
7
Views
1K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 3 ·
Replies
3
Views
1K
Replies
2
Views
1K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 8 ·
Replies
8
Views
2K
Replies
2
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K