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1. ### Convergence of the Arctangent Integral

Yup! Thanks for all the help! This has cleared things up for me.
2. ### Convergence of the Arctangent Integral

When I say the second integral is symmetric, I guess what i mean is that t is approaching infinity on both sides. But for the first integral, you can interpret it as an integral from a to 0 plus an integral from 0 to b, with 'a' going to negative infinity while 'b' goes to infinity. In that...
3. ### Convergence of the Arctangent Integral

Hmm. Can you explain to me this then? http://www.wolframalpha.com/input/?i=integral+of+arctan%28x%29+from+negative+infinity+to+infinity The limit (2nd integral) converges to zero when I test it on mathematica tho. Also, what is the Cauchy Principal Value? That seems to be zero.
4. ### Convergence of the Arctangent Integral

Thanks for the replies guys. I thought about the question a bit more. I believe that the two integrals are not the same. The first one can be split into the integral from -Infty to 0 + the integral from 0 to +Infty. These two integrals are both divergent and so the sum is divergent (there is...
5. ### Convergence of the Arctangent Integral

Homework Statement Is $\intop_{-\infty}^{\infty}\arctan(x)\, dx$ convergent? What about $\lim_{t\rightarrow\infty}\intop_{-t}^{t}\arctan(x)\, dx$? Homework Equations The Attempt at a Solution I think the first integral may actually be divergent the way its written and the second one...