Example 1
Look at the picture below, which shows a region A within a region B.
If the area of region A is infinite, what does that tell us about the area of region B?
Example 2
Look at the picture below, which shows a region A within a region B.
If the area of region B is finite, what does that tell us about the area of region A?
Example 3
Look at the picture below, which shows a region A within a region B.
If the area of region A is finite, what does that tell us about the area of region B?
Example 4
Look at the picture below, which shows a region A within a region B.
If the area of region B is infinite, what does that tell us about the area of region A?
Example 5
From the graph below, determine if each integral converges, diverges, or if its behavior cannot be determined.
(a) 
(b) 
(c) 
(d) 
(e) 
(f) 
, but since
and
and
doesn't help, because
Example 6
From the graph below, determine if each integral converges, diverges, or if its behavior cannot be determined.
(a) 
(b) 
(c) 
(d) 
(e) 
(f) 
is the same as the function 
. We know the integral of this function from 0 to 1 converges, and the integral of this function from 1 to ∞ diverges.
and
that doesn't help us at all.
, we can't tell what
and 
Example 7
From the graph below, determine if each integral converges, diverges, or if its behavior cannot be determined.
(a) 
(b) 
(c) 
(d) 
(e) 
(f) 
on (0,1] and 
on [1,∞) and
on [0,1), but the integral
on [0,1), but 
on [1,∞).
on [1,∞).
Example 8
If 0 < f (x) and
converges, does
converge or diverge?
Example 9
Use the graph to determine if 
converges or diverges.
, and
Example 10
Does 
converge or diverge?
