Problem with setting the region of integration

[Amaelle]

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!

 

[andrewkirk]

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!

 

[Amaelle]

that was an amzing shot! thanks a million!