Finding Centroid of Triangle in First Quadrant

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Homework Help Overview

The discussion revolves around finding the centroid of a triangular region in the first quadrant, specifically bounded by the line 4x+y=4, the x-axis, and the y-axis.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are discussing the appropriate limits of integration for calculating the centroid, questioning whether the limits for dy and dx are set correctly. There are attempts to clarify the relationship between x and y in the limits.

Discussion Status

The discussion is ongoing, with participants providing feedback on each other's attempts to set up the problem. Some guidance has been offered regarding the limits of integration, but there is no explicit consensus on the correct setup yet.

Contextual Notes

Participants are considering the implications of their chosen limits and the necessity of sketching the region of integration to better understand the problem setup.

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Homework Statement


Find the centroid of the triangular region in the first quadrant bounded by the line 4x+y=4, the x-axis, and the y-axis.


Homework Equations


\int\int\deltadA
xbar = My/M
ybar = Mx/M

The Attempt at a Solution


Is the boundary for the dy from 0 to 4, and dx from 0 to 4-4x?
 
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No, your limits for x can't contain x. They can only depend on y.
 
so its y-4/4?
also are my limits for dy correct?
 
No, that's not quite correct either. (I assume you mean (y-4)/4, not y-1.) You should always plug in a few values to do a sanity check. In this case, when y=0, you'd get a negative answer.

Your limits for y are fine. (But I'll note I'm saying this under the assumption that you set things up correctly.)

Did you draw a sketch of the region of integration?
 
the region would be the triangle from y=4 to y=0 and x=0 and x=1 right?
and is the limit 4-4x?
 

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