Question

What's the difference between these two integrals?

Answer 1

\[\int\limits_{b}^{a}|f(x)|dx \] vs \[\int\limits_{b}^{a}f(x)dx\]

Answer 2

One has an absolute value symbol around the f(x) one doesnt

Answer 3

All it means is that anything that lies below the x-axis is flipped up right?

Answer 4

yes. it also means if you know the function, you have to integrate separately over the intervals where it is positive and negative