Question

Determine whether each of the following integrals is convergent or divergent. Evaluate those that are convergent.

Intergral 2xe^-x^2 dx from x = infinite to x = 0

Answer 1

please clarify
\[\int_{0}^{\infty} 2xe^{-x^2}\]

is this the integral?
if so then
\[-e^{-x^2} |_{0}^{\infty}\]
it is an improper integral you have to write it as a limit, but i will skip that,
so
\[-e^{-\infty^2}-(-e^{-0^2})=-0+1=1 \]

Answer 2

I was soooooooooooooooooooooooooooooooo close

Answer 3

hahahahha, I've had the feeling. Glad to be of help.

Answer 4

can I give you one more to check

Answer 5

sure

Answer 6

Well the first one is convergent correct?

Answer 7

And the next question is intergral e^x from x = 100 to x = infinite

Answer 8

The first one is convergent, that is correct.

Answer 9

\[\int_{100}^{\infty} e^x = e^x|_{100}^{\infty}=e^{\infty}-e^{100}=\infty \]
so it diverges.

Answer 10

I'm getting good at this

Answer 11

That's good news for mathematicians.