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tomiko
 2 years ago
when is it impossible to find the definite integral of a function?
tomiko
 2 years ago
when is it impossible to find the definite integral of a function?

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Mani_Jha
 2 years ago
Best ResponseYou've already chosen the best response.1If 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

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

Mani_Jha
 2 years ago
Best ResponseYou've already chosen the best response.1yes, stating the reason if possible

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

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0Some 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

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0And, 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.
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