[Graphics:../Images/index_gr_40.gif]

Answer:

       [Graphics:../Images/index_gr_41.gif]
measures the area under the the plot of
       [Graphics:../Images/index_gr_42.gif]
and above the segment [Graphics:../Images/index_gr_43.gif] on the [Graphics:../Images/index_gr_44.gif]-axis.

Here's a picture of the area measured by [Graphics:../Images/index_gr_45.gif]:

[Graphics:../Images/index_gr_46.gif]

[Graphics:../Images/index_gr_47.gif]

This integral calculates  the area of a trapezoid with

[Graphics:../Images/index_gr_48.gif]

Consequently the area measurement
       [Graphics:../Images/index_gr_49.gif]
in square units is given by:

[Graphics:../Images/index_gr_50.gif]
[Graphics:../Images/index_gr_51.gif]

Mathematica can also handle this measurement directly:

[Graphics:../Images/index_gr_52.gif]
[Graphics:../Images/index_gr_53.gif]

Good going.


Converted by Mathematica      November 16, 1999