Area under a Curve
The area between
the graph of y = f(x)
and the xaxis is given by the definite
integral below. This formula gives a positive result
for a graph above the xaxis, and a
negative result for
a graph below the xaxis.
Note: If the graph
of y = f(x) is
partly above and partly below the xaxis, the formula
given below generates the net area. That is, the area above
the axis minus the area
below the axis.
Formula: 

Example 1: 
Find the area between y = 7 – x^{2} and
the xaxis
between the values x = –1 and x =
2.

Example 2: 
Find the net area between y = sin x and
the xaxis between the values x = 0
and x = 2π.

See
also
Area
between curves, area using
parametric equations, area
using polar coordinates
