Improper Integrals - Plugging Infinity into Inverse Tangent

[bdthomso]

I have an improper integral problem. I've integrated the orginal problem and my answer is arctan(x^3), but I have to evaluate it from -infinity to 0 and then again from 0 to infinity. I do not know how to put infinity into tangent though.

Thanks

 

[daon2]

You dont plug it in, you should probably know from a prior trig class that arctangent has two horizontal asymptotes.

 

[HallsofIvy]

I have an improper integral problem. I've integrated the orginal problem and my answer is arctan(x^3), but I have to evaluate it from -infinity to 0 and then again from 0 to infinity. I do not know how to put infinity into tangent though.

Thanks

You don't put "infinity" into anything.. It is NOT a number, it is just shorthand for "unbounded". And you don't put anything into "tangent", you put it into arctangent. What happens to \(\displaystyle tan(\theta)\) as \(\displaystyle \theta\) approaches \(\displaystyle \frac{\pi}{2}\)?