Question

When an integral is zero is it convergent or
divergent?

Answer 1

if we are talking about the integral itself
the question is do you think 0 is a number ?

Answer 2

I would say yes.....

Answer 3

0 is a number so yes if your integral is 0 then your integral converges

Answer 4

if it was infinity or -infinity then would diverge
these aren't numbers

Answer 5

ok but what about this integral then? \[ \int\limits_{-\pi/2}^{\pi/2} cscx \]
I got a value of zero but wolfram said it doesn't converge....

Answer 6

heres my work

Answer 7

@freckles

Answer 8

wait nevermind, its a type two improper integral

Answer 9

on the given interval csc(x) doesn't exist at x=0

Answer 10

\[\int\limits_\frac{-\pi}{2}^0 \csc(x)+\int\limits_{0}^{\frac{\pi}{2}} \csc(x) dx\]

Answer 11

you need to evaluate both of these improper integrals

Answer 12

well you don't necessarily to evaluate both
if you find one diverges it is all over with and not necessary to evaluate the other

Answer 13

anyways I'm going to get food
bbl if you have more questions