Answer:
Here's a picture of the area measured by
:
![[Graphics:../Images/index_gr_57.gif]](../Images/index_gr_57.gif)
![[Graphics:../Images/index_gr_58.gif]](../Images/index_gr_58.gif)
Better find out where the area goes from positive to negative:
![[Graphics:../Images/index_gr_59.gif]](../Images/index_gr_59.gif)
The measurement
![]()
of the triangular area on the left is negative because it is below the
-axis:
![[Graphics:../Images/index_gr_63.gif]](../Images/index_gr_63.gif)
Now look at the triangle on the right:
![[Graphics:../Images/index_gr_65.gif]](../Images/index_gr_65.gif)
![[Graphics:../Images/index_gr_66.gif]](../Images/index_gr_66.gif)
The measurement
![]()
of the triangular area on the right is positive:
![[Graphics:../Images/index_gr_68.gif]](../Images/index_gr_68.gif)
Consequently,
![]()
is given by:
![[Graphics:../Images/index_gr_71.gif]](../Images/index_gr_71.gif)
Mathematica can calculate
![]()
directly:
![[Graphics:../Images/index_gr_74.gif]](../Images/index_gr_74.gif)
Got it, and it wasn't very hard.