Problem with setting the region of integration

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The discussion centers on confusion regarding the limits of integration for a specific set of integrals. Participants clarify that the upper limit on the outer integral can be set to b/a instead of c, even if c is greater than b/a. The area of integration is defined as a triangle with vertices at (0,0), (0, b/a), and (b,0). It is noted that the value of c is irrelevant to the calculation, suggesting it may have been included to mislead. Overall, the focus is on understanding the correct boundaries for integration in the given context.
Amaelle
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Homework Statement
look at the image below!
Relevant Equations
double integrals
Good day !
I have a problem with the solution of the floowing integrals
Indeed i don't understand why they choose such borders for integral
b/a<c
y<c
doesn't mean that y<b/a !
many thanks in advance!

1614189909864.png
 

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Amaelle said:
doesn't mean that y<b/a !
For ##(x,y)\in\Omega##, yes that is correct. That's why they can set the upper limit on the outer integral to ##b/a## rather than ##c##, even though ##c## may be greater than ##b/a##.

The area of integration is a triangle with vertices (0,0), (0, b/a), (b,0).

Given that c>b/a, the value of c is not used in the calculation. I think they just put it in the question to confuse people!
 
that was an amzing shot! thanks a million!
 
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