MA 126 Chapter 1: Improper Integrals III
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Let"s take a look at a couple more examples. Example 2 determine if the following integral is convergent or divergent and if it"s convergent find its value. 11xdx 1 1xdx. So, the first thing we do is convert the integral to a limit. So, the limit is infinite and so the integral is divergent. If we go back to thinking in terms of area notice that the area under g(x)=1xg(x)=1x on the interval [1, )[1, ) is infinite. This is in contrast to the area under f(x)=1x2f(x)=1x2 which was quite small. There really isn"t all that much difference between these two functions and yet there is a large difference in the area under them.
