When integrating with respect to y to find the area of a region, how do you know which function is the upper boundary?

Question

7thgrader · Answer

Make sure you didn't give any medals on a post yet, and open the same post in a new tab, then give a medal to two different people.

anonymous · Answer

What???

kainui · Answer

Let's say you're integrating y=x^2 from 0 to 4 on y, then it could look like this |dw:1424110231092:dw|

anonymous · Answer

Yes

kainui · Answer

Really all we're doing is taking y=x^2 and renaming the y and x to be the others like this x=y^2 and solving for our new "y" as y=sqrt(x) and integrating from 0 to 4. See, not really doing anything too crazy I hope.

anonymous · Answer

Yes

anonymous · Answer

But how do you determine which one is the upper or lower boundary? I tried flipping the paper and going with whichever one is on top, but that ALWAYS gives me the wrong one

anonymous · Answer

|dw:1424110990160:dw|