If is some region in the plane and
is a
(continuous) function taking positive values, then
the volume of
is the
integral
More generally, if is any continuous function, then
is the signed volume of
the solid bounded by
.
If
is the unit square and
, then the solid bounded by
over
is the unit
cube. So,
.
If
(where
are constants and
and
are continuous
functions of
), then
Here,
is itself a function of
.
Suppose and
.
Compute
Compute
Compute