We next evaluateeachimproperintegral.Integratingthe first integralon the right handside,
The integraldivergesbecause and are not defined,and thus thereis no reasonto evaluate
the secondintegral.We concludethat the originalintegraldivergesand has no finitevalue.
Example4:
Evaluate.
Solution:
So the integralconvergesto.
Example5:
In Chapter 5 you learned to find the volume of a solid by revolving a curve. Let the curve be
and revolvingaboutthe -axis.Whatis the volumeof revolution?
Solution: