For , compute the following integral:

Since we are taking the integral of an absolute value, first we want to determine on which intervals is positive and on which it is negative. We have,

Now must consider two cases. First, if , then,

In the other case, that , then,

Hello, Can you please explain the function (the absolute function) that you have in the 1st line? Why is the function between -2pi/3 and 2pi/3 negative ?