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

Question

mani_jha · Answer

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

anonymous · Answer

so 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 · Answer

yes, stating the reason if possible

anonymous · Answer

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

turingtest · Answer

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

turingtest · Answer

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.