Question

when is it impossible to find the definite integral of a function?

Answer 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

Answer 2

so when i have a question like the above i can just state it's impossible find the def integral of the this function?

Answer 3

yes, stating the reason if possible

Answer 4

great! thanks. :). can you give another instance where it's impossible to find the integral?

Answer 5

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

Answer 6

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.