>>1353136lmao its been a while since ive had calc I memories again
basically look at the graph of your non-absolute valued integrand. notice when it crosses the x axis? (the zeros)? Solve the non absolute-valued integrand for these zeros, and make a sign chart (if the function is neg or pos in this range of 2 zeros) with these zeros
Now, split the bounds of integration by these zeros, and integrate your function without absolute values at each of these ranges. Then, before you add them all up, put a negative per your sign chart at each of these integration results.
For instance, say you want to integrate "|f(x)|" from a to b, with zeros y and z within the bounds a and b. Hypothetically, this is our sign chart
f(x) value | - - (-) - - | - - - (+) - - | - - (-) - - |
a y z b
So your integral becomes
[math:lit]\int_a^b |f| dx = (-)\int_a^y f dx + (+)\int_y^z fdx + (-)\int_z^b fdx[/math:lit]
