How is this improper integral convergent?
$$\int\limits_{\pi/2}^{\pi}34\csc(x)dx$$

Question

How is this improper integral convergent?
$$\int\limits_{\pi/2}^{\pi}34\csc(x)dx$$

anonymous · Answer

I have an attempt. If you need to go, its OK. It may take a while to post.

rogue · Answer

Do you need help integrating the cosecant? Or evaluating the definite?

wasiqss · Answer

Integration of Csc = Ln(csc-cot)

rogue · Answer

Isn't the integral of cosecant -ln (cot + csc)?

rogue · Answer

Anyways, I have to go, so I'll give you a few hints before I leave.

In order to integrate cosecant, multiply it by:$$\frac {\csc x + \tan x}{\csc x + \tan x}$$and use u-sub.

In order to evaluate the definite integral, let b be the upper limit of integration because csc is undefined at pi and make it into a limit. lim b-->pi

Good luck! :)

rogue · Answer

Oops, I meant $$\frac {\csc x + \cot x}{\csc x + \cot x}$$

anonymous · Answer

http://i1084.photobucket.com/albums/j409/QRAWarrior/MATA36/MATA36-A4-Question2.png I actually passed the part of integrating cscx. I got stuck at an "ln" expression @asnaseer

anonymous · Answer

@dpaInc

anonymous · Answer

Ok perhaps I missed out a (-1) somewhere, but I will still run into that problem in the argument of the natural log.

anonymous · Answer

yeah, missing a -1 in the ln expression should be -ln(cscx-cotx) or ln(1/(cscx-cotx))

anonymous · Answer

I think the helpers gave up...