Lecture 21 : Area between two curves [Section 21.2]
21.2
Area between two Curves
In the previous module, we defined the area under a curve , where is a non-negative Riemann integrable function. We can view this as the area between the curves and the lines . This can be extended to the area between any the two curves.
21.2.1
Definition:
Let
be two curves, where are Riemann integrable and ---------- (9)
We define the area bounded by and the lines by the formula .
In general, where (9) need not hold, the area bounded by and the lines is defined by the formula .
, where 
is a non-negative Riemann integrable function. We can view this as the area between the curves 
and the lines 
. This can be extended to the area between any the two curves. 
are Riemann integrable and 
---------- (9)
and the lines 
by the formula 
. 
and the lines 
is defined by the formula 
.
