Question

Integral of absolute functions: (Next post)

Answer 1

I know how to solve integrals, but what do I do when I face one of these?
\[f(a) = \int\limits_{0}^{a} |x(x-a)|\ dx \le0\le a \le 2\] and\[S = \int\limits_{0}^{2} |x(x-1)|dx\]

Answer 2

Do I have to split normally on the intervals that they change signals?

Answer 3

on the first integral the upper limit is 2. Sorry that I didn't fix it :P

Answer 4

between 0 and 1 x(x-1) <0 and betwen 1 and 2 x(x-1)>0

Answer 5

so you have to split them on intervals that they change signals due to definition of absolute magniyude