Transcript Definite Integrals

Definite Integrals
5.6
Area Between Curves
Now to work
So far we have given definite integrals –
4
for instance
2
16

x
dx

0
But what does this mean?
Since integration gives us the area under a curve,
that problem is specifically asking for the area of
the curve
y = 16 – x2
(0,16)
4
2
16

x
dx

0
(4,0)
Now you will see these same problems in word
problem format. You might have to determine
endpoints, but this is easy.
Advice
As always, take it if you want. I would
suggest a quick sketch of the graph so
that you can get an idea of all intercepts
so you know the area of integration.
Don’t remember how to graph? Plot points.
Examples
1. Find the area between the curve
2
y  16  x and the x axis.
2. Find the total area of the region between
3
the curve y  3x  3x and the x axis.
3. Find the total area of one cycle of the cos x
graph.