How to evaluate a double integral over a bounded region?

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SUMMARY

The discussion focuses on evaluating the double integral of the function 2x + y over the bounded region R defined by the lines y = 3x, 2x + y = 5, and the axes x = 0 and y = 0. Participants identify a potential error in the problem statement, suggesting that the integral cannot yield a negative result given the defined region in the first quadrant. The provided answer of -2875/6 is contested, indicating a misunderstanding of the boundaries of region R.

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  • Understanding of double integrals in calculus
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  • Knowledge of the Cartesian coordinate system
  • Ability to analyze linear equations and their intersections
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  • Study the method of evaluating double integrals using iterated integrals
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Students and educators in calculus, mathematicians focusing on integral calculus, and anyone involved in solving complex integral problems in bounded regions.

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
 
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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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