Different results while switching the order of integration

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Switching the order of integration in a double integral can lead to different results if the limits are not correctly applied. The upper limits for the integration should be y when integrating with respect to x and x when integrating with respect to y. Misunderstandings can arise from misreading the problem or the setup of the integral. A video resource was shared that clarified the confusion effectively. Properly understanding the limits of integration is crucial for obtaining consistent results.
Amaelle
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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
20200824_143133.jpg
20200824_143118.jpg
 
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the upper limits should be y in the first instance (for x) and x in the second (for y)
 
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this is what is written no? could you please explain more i still didn't get your point?
 
Sorry I misread your images. I will instead send you to a video as the easiest route
 
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Great video, thanks a million it answered perfectly my question!
 
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