5.1. Area Between Two Curves http://www.ck12.org

Find the area of the region enclosed byx=y^2 andy=x− 6.
Solution:

Figure 4
As you can see from Figure 4, the left boundary isx=y^2 and the right boundary isy=x− 6 .The region extends
over the interval− 2 ≤y≤ 3 .However, we must express the equations in terms ofy.We rewrite

x=y^2

x=y+ 6

Thus

A=

∫ 3

− 2 [y+^6 −y

(^2) ]dy

[y 2
2 +^6 y−
y^3
3

] 3

− 2

=^1256.

Multimedia Links

For a video presentation of the area between two graphs(14.0)(16.0), see Math Video Tutorials by James Sousa, Are
a Between Two Graphs (6:12).