Example 9

Find

The function 1/x² + 1/(x - 1)² is continuous on the open interval (0, 1) but discontinuous at both endpoints. The indefinite integral is

We have

Similarly we find that

In this situation we may write

and we say that the region under the curve in Figure 6.7.9 has infinite area.

Figure 6.7.9

Remark In Example 9 we are faced with a sum of two infinite limits. Using the rules for adding infinite hyperreal numbers as a guide we can give rules for sums of infinite limits.