• Support PF! Buy your school textbooks, materials and every day products Here!

Improper integral convergence or divergence.

  • #1

Homework Statement



Use Comparison Theorem to determine whether the integral is convergent or divergent:

integral from 0 to infinity of: arctan(x) / (2 + e^x)

Should look like this: http://bit.ly/cAhytV [Broken]

Homework Equations



--

The Attempt at a Solution




I tried to compare this with the integral from 0 to infinity of 1/e^x, but that didnt succeed since 1/e^x converges and the given function is less than 1/e^x. I am not sure what to compare this with
 
Last edited by a moderator:

Answers and Replies

  • #2
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,544
756

Homework Statement



Use Comparison Theorem to determine whether the integral is convergent or divergent:

integral from 0 to infinity of: arctan(x) / (2 + e^x)

Should look like this: http://bit.ly/cAhytV [Broken]

Homework Equations



--

The Attempt at a Solution




I tried to compare this with the integral from 0 to infinity of 1/e^x, but that didnt succeed since 1/e^x converges and the given function is less than 1/e^x. I am not sure what to compare this with
Not sure why you chose 1/ex since [itex]\arctan x \le \pi/2[/itex] but not bounded by 1.

Anyway, why wouldn't you have succeeded if your integral is less than a known convergent integral? Your problem would be if your unknown integral was greater than a known convergent integral.
 
Last edited by a moderator:
Top