How to evaluate a double integral over a bounded region?

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Discussion Overview

The discussion revolves around evaluating the double integral of the function 2x + y over a bounded region R defined by the lines y = 3x, 2x + y = 5, and the axes x = 0 and y = 0. Participants explore the boundaries of the region and express concerns about the formulation of the problem.

Discussion Character

  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant asks how to evaluate the double integral 2x + y dA over the specified region R.
  • Another participant presents a similar question but with a slight variation in the equation, suggesting a potential typographical error.
  • A later reply corrects the equation to 2x + y = 5, indicating a possible misunderstanding in the problem statement.
  • Participants discuss the boundaries of region R, questioning how it can be defined by both axes and the two lines simultaneously.
  • One participant expresses agreement that there may be an error in the problem as presented, citing a given answer that seems inconsistent with their understanding.
  • Another participant notes that the lines y = 3x and 2x + y = 5 form a triangle in the first quadrant, asserting that the integral cannot yield a negative value over this region.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the formulation of the problem and the boundaries of the region R. There is no consensus on the correctness of the problem statement or the provided answer.

Contextual Notes

There are unresolved questions about the definitions and boundaries of the region R, as well as the correctness of the equations provided in the problem statement.

mduffy
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how do I evaluate the double integral 2x + y dA over the region R bounded by y = 3x, 2X + y = 5, x = 0, and y = 0
 
Last edited:
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mduffy said:
how do I evaluate the double integral 2x + y dA over the region R bounded by y = 3x, 2X = y = 5, x = 0, and y = 0

Check this entry ...
 
skeeter said:
Check this entry ...
Thanks...should be 2x + y = 5
 
over the region R bounded by y = 3x, 2X + y = 5, x = 0, and y = 0

Region R is bounded by either x = 0 or y = 0 ... how is it bounded by both axes and the two given lines?
 
skeeter said:
Region R is bounded by either x = 0 or y = 0 ... how is it bounded by both axes and the two given lines?

Agreed! I think the teacher made a mistake with the problem. The given answer (no steps shown) is -2875/6. I am thinking there is an error in how the question is asked.
 
The lines y= 3x and 2x+ y= 5 form one triangle with x= 0 and another with y= 0. But both of those are in the first quadrant where x and y have only positive values. The integral of (2x+ y) dA can't be negative over either of them.
 

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