Section 6.1 - Areas
MATH 1920
The area Aof the region bounded by the curves yfx,ygx, and the lines xaand xbwhere f
and gare continuous and fx≥gxfor all xin a,bis
Aa
bfx−gxdx
f(x)
g(x)
x = a x = b
Find the ares enclosed by the given curves.
1.yx−1andy1−x2
2.fxx3−9xand gx7x
-5 -4 -3 -2 -1 1 2 3 4 5
-80
-60
-40
-20
20
40
60
80
fg
3. Sometimes it is easier or necessary to integrate with respect to the y-axis. In this case we need to regard x
as a function of yas in this example:
xy2−6andy−x.
4. Area enclosed by parametric curves. See Example 6 on page 445.
1
