Question

Find the exact value of the equation:

(integral from 10 to infinity) 1/((z^2) - 4)

Answer 1

It's critically important to ensure you've correctly communicated the problem at hand to potential helpers. Here's my interpretation:\[\int\limits_{10}^{\inf}\frac{ 1 }{ z^2-4 }dz.\](Don't forget that "dz.")
Does this ring a bell? What would you consider to be the first step in integrating this?
@bebong

Answer 2

to the interval, nothing is restricted, so that no need to take improper integral, right? however, without it, I got stuck at the result which is \(\dfrac{-1}{4}ln(\dfrac{z+2}{z-2})\) . How to plug in the upper limit in??
If taking improper integral, I got 0.10136
However, as I argued above, I can't solve the problem on that way. Please, explain me

Answer 3

I note that you have factored z^2-4, because that's where your z+2 and z-2 came from. Good.

Think about this: What is the limit of (z+2)(z-2) as z approaches infinity?

Answer 4

0

Answer 5

Please try again on that one. the limit is not zero.

Answer 6

It is, because it is in denominator 1/ it, not itself.

Answer 7

Too bad we have to have a little argument this early in the game.