what is the value of
integral ( from 0 to 2pi ) |arcsin(sinx)| dx
where | | means absolute value
..answer is pi*pi/2.0 ;
means the value of between and such that . So when
When you should use the fact that to deduce that .
For , will be given by yet another formula, which I'll leave you to think about.
Once you have the formulas for on the three different intervals, you should find it comparatively easy to take their absolute values and integrate over the corresponding intervals.
When you have done this, it would be a good idea to check your answer by drawing the graph of on the interval from to . It should consist of straight line segments, and the area under the graph will consist of a number of triangles. You can then check that your value for the integral is correct by calculating the total area of these triangles using the formula "half base times height".