Calculating work done by a force field using Green's Theorem on a triangle

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Homework Help Overview

The problem involves using Green's Theorem to calculate the work done by a specified force field in moving a particle around a triangular path defined by three vertices. The force field is given as F = <5x²y³, 7x³y²>.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the setup of the integral needed to apply Green's Theorem, with one participant attempting to integrate 6x²y² over the triangle. There are questions about the limits of integration and the correctness of the function being integrated.

Discussion Status

Some participants confirm the setup is correct, while others suggest re-evaluating the integral limits and the function used. There is an ongoing exploration of the calculations and interpretations of the triangle's boundaries.

Contextual Notes

One participant notes that the line y=2x is not a side of the triangle, indicating a potential misunderstanding of the triangle's geometry. This highlights the importance of accurately defining the region of integration.

kasse
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Homework Statement



Use Green's Theorem to calculate the work done by the force field

F = <5x2y3, 7x3y2>

in moving a particle counterclockwise once around the triangle with vertices (0, 0), (3, 0) and 0, 6).



2. The attempt at a solution

I must integrate 6x2y2 over the triangle, right? I then get 1944 as the answer, but the correct answer is 972/5. What is wrong?
 
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Yep, you got it set up all right. But I do get 972/5 for the double integral of 6*x^2*y^2 over the triangle. Check that again. Post how you worked it out if you can't get it.
 
Dick said:
Yep, you got it set up all right. But I do get 972/5 for the double integral of 6*x^2*y^2 over the triangle. Check that again. Post how you worked it out if you can't get it.

OK, i integrate with respect to y first, which gives 2x^2*y^3. The limits are y=0 and y=2x, so I now have to integrate 16x^5 with respect to x. This gives (8/3)x^6, and the limits are x=0 and x=3, so that the answer is 1944.
 
y=2x isn't one of the sides of your triangle. y=6-2x is. Draw a picture.
 
Lol, thanks!
 

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