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Mani_JhaBest ResponseYou've already chosen the best response.1
If the function doesn't exist in an interval. For example, \[\int\limits_{1}^{0}\ln xdx\] is meaningless. log is defined only for positive numbers
 one year ago

tomikoBest ResponseYou've already chosen the best response.0
so when i have a question like the above i can just state it's impossible find the def integral of the this function?
 one year ago

Mani_JhaBest ResponseYou've already chosen the best response.1
yes, stating the reason if possible
 one year ago

tomikoBest ResponseYou've already chosen the best response.0
great! thanks. :). can you give another instance where it's impossible to find the integral?
 one year ago

TuringTestBest ResponseYou've already chosen the best response.0
Some integrals, like\[\int_a^b e^{kx}x^{1/2}dx\]and\[\int_a^b\sin(x^2)dx\]have no closed form, and have to be written in terms of the error function
 one year ago

TuringTestBest ResponseYou've already chosen the best response.0
And, as Mani said, if the interval contains a singularity, like\[\int_{1}^1\frac{dx}x\]is undefined because there is a singularity at x=0. In this case, if you want an answer you can use the Cauchy principle value, which in this case gives 0. In principle though, this integral does not converge.
 one year ago
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