Does this integral converge or diverge, and how?
$$\int\limits_{\pi/2}^{\pi}34(cscx)dx$$

Question

Does this integral converge or diverge, and how? 
$$\int\limits_{\pi/2}^{\pi}34(cscx)dx$$

anonymous · Answer

@TuringTest

anonymous · Answer

it diverges because the graph blows up to infinity if you graph the answer

anonymous · Answer

That was what I was thinking, until: http://www.wolframalpha.com/input/?i=integral+pi%2F2+to+pi+34cscx @sonofa_nh

anonymous · Answer

well even that graph...starts at like 48...goes straight..then blows up..so it would diverge

anonymous · Answer

if it was convergent it would dive down close to zero and stay constant

anonymous · Answer

i think....it has been a few years since i've taken calc 2....don't really analyze integrals after that class...just do integrals from time to time

anonymous · Answer

@TuringTest I got stuck when evaluating the ln's

anonymous · Answer

@dpaInc 
@Zarkon 
@ParthKohli 
@FoolForMath 
@AccessDenied 
@SmoothMath 
@KingGeorge 
@TuringTest

kinggeorge · Answer

You're given a definite integral. Unless I'm severely mistaken, those should always converge for the same reason that the sum of a finite series is always finite.

anonymous · Answer

No. Definite integrals do not always converge....

kinggeorge · Answer

Interesting. May I have an example? 

(I'm assuming the function is defined and continuous on the interval as well)

anonymous · Answer

Consider: 
$$\frac{-\pi}{2}\int\limits_{0}^{\infty}(\frac{1}{2} - e^{-x})^{-1} dx $$

kinggeorge · Answer

In that case, I don't know how to make a convincing argument that this converges or diverges.