BC 3
Improper Integrals 2
Name:
We saw on the previous worksheet that the bounded by the graphs of
1
x  1, y  0, and f ( x)  x is finite. We now wish to find the exact area of this region.
2
We know from our previous work that the area must be less than 4 – the area of the 2  2

1
square. We can also reason the area is greater than zero. Let us use  x dx to represent
2
1
this area. This is called an improper integral and it represents an area (though the area of
an unbounded region).
f ( x) 
1
2x

1. Find the value of
1
2
x
dx with a reasonable explanation.
1
IMSA BC 3
Improper Integrals 2.1
Fall 14
f ( x) 

2. Find the value of
1
x
1
 x dx with a reasonable explanation or explain why there is no
1
reasonable value.
IMSA BC 3
Improper Integrals 2.2
Fall 14