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Originally Posted by fuzzybottom
i tried to use:
-[(x-1)²]^(1/2) +1
and integrate that but it got messy, and i'm not sure if thats a good way to go about it because of the exponents and how they might distribute.
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I guess that would work, but it is ugly. I think using abolute values would be much cleaner:
f'(x) = -|x-1|+1
Then if you need to integrate it it would break down into pieces:
x: 0<x<=1
-x+2: 1<x<2
Which is what you have already. It really isn't that uncommon for integrals to be evaluated piecewise, and it makes your job a lot easier than messing around trying to get one nice function. After all the function isn't smooth, so I wouldn't try to integrate it as if it were.