How Can You Evaluate This Complex Double Integral?

Click For Summary

Homework Help Overview

The discussion revolves around evaluating a complex double integral involving the function \( e^{\frac{x}{y}} \) with specified limits of integration. The integral is presented in the context of a problem from a textbook.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the evaluation of the integral, with one attempting a substitution and expressing results. Others question the correctness of the limits of integration and seek clarification on the original problem statement.

Discussion Status

The discussion is ongoing, with some participants providing insights into their calculations while others are questioning the assumptions made regarding the limits of integration and the interpretation of the problem.

Contextual Notes

There is a reference to a solution from the text that suggests a different outcome, which raises questions about the validity of the approaches taken by the participants.

nameVoid
Messages
238
Reaction score
0
<br /> \int_{1}^{2}\int_{y}^{y^3}e^{\frac{x}{y}}dxdy<br />
<br /> \int_{1}^{2}ye^{y^2}-eydy<br />
taking u = y^2
<br /> \frac{1}{2}\int_{1}^{4}e^udu-\int_{1}^{2}eydy<br />
<br /> e^4/2-2e<br />

 
Physics news on Phys.org
...?
 
What is your question?
What you have done seems to make mathematical sense assuming your limits of integration is correct .
 
the problem directly from the text reads int int e^(x/y) dA, 1<=y<=2 , y<=x<=y^3 shows a solution of 6
 

Similar threads

Replies
4
Views
3K
  • · Replies 19 ·
Replies
19
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
1
Views
3K
Replies
2
Views
1K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
3
Views
2K
Replies
6
Views
3K
  • · Replies 7 ·
Replies
7
Views
2K