BC 3
Improper Integrals 1
f ( x) 
Name:
1
2x
Look at the “unbounded” shaded region shown above. This is the region that is bounded
1
by the graphs of x  1, y  0, and f ( x)  x . Suppose that we have a 2  2 square and a
2
pair of scissors. Is it possible to cover the entire shaded region with 2  2 square? You
may make infinitely many cuts and you need not cover the region carefully/precisely, you
need only make certain that the entire shaded region is covered.
Explain carefully how you would do this or why this would be impossible.
IMSA BC 3
Improper Integrals 1.2
Fall 14
f ( x) 
1
x
1
. Look at the “unbounded”
x
1
shaded region above that is bounded by the graphs of x  1, y  0, and f ( x)  . Is it
x
possible to cover the entire shaded region with 2  2 square? Again, you may make
infinitely many cuts and you need not cover the region carefully/precisely.
Explain carefully how you would do this or why this would be impossible.
We now repeat this problem with the function f ( x ) 
IMSA BC 3
Improper Integrals 1.2
Fall 14