Different results while switching the order of integration

[Amaelle]

Homework Statement

∫y dA where the region is the triangle A(0,0) B(0,1) C(1,1)

Relevant Equations

y=x
0<x<1 and 0<y<1 and y=x

my Problem is that I get a different result when I switch the order of integration (X over Y), I couldn't spot the mistake, any help would highlyu appreciated

 

[hutchphd]

the upper limits should be y in the first instance (for x) and x in the second (for y)

 

[Amaelle]

this is what is written no? could you please explain more i still didn't get your point?

 

[hutchphd]

Sorry I misread your images. I will instead send you to a video as the easiest route

 

[Amaelle]

Great video, thanks a million it answered perfectly my question!