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

1. Mani_Jha

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

2. tomiko

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

3. Mani_Jha

yes, stating the reason if possible

4. tomiko

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

5. TuringTest

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

6. TuringTest

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.