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how would you evaluate this integral lets say if we wish to calculate the integral from 1 to infinity of 1 over x dx how can we get the answer and this particular integral is it convergent or is it divergent how do we tell well if we get a finite number l lets say if the limit exists that would mean that it converges to a value however lets say if we dont get a finite number lets say we get infinity then we can say the integral is divergent so this is called an improper integral when you see infinity either in the lower or in the upper limit of the integral sign so how do we evaluate this well first we need to replace infinity with some variable which in this case will be t so were going to express it as a limit so were going to say the limit as t approaches infinity of the integral one to t one over x dx now what is the anti-derivative of one over x well we know it to be ln x but first we need to rewrite the limit expression so we have the limit as t approaches infinity ln x e
