Let's say you have a function that is continuous in (a,b] but discontinuous at x=a and you integrate it from a to b.(adsbygoogle = window.adsbygoogle || []).push({});

For example, [itex] \int^{1}_{0} \frac{1}{\sqrt{x}}dx [/itex]

I understand that the integral exists, and it can be easily computed by using the limit as x approaches 0 from the positive side.

What bothers me is the intuition of the problem. If we divide the area up into infinite rectangles, it seems that some of the rectangles approaching the lower limit are of infinite length, so that their area must also be infinite? I can't fathom how you can add up these rectangles that approach lengths of infinity.

BiP

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# Intuition of improper integrals of type II

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