Question

Help please. Question attached.

Answer 1

Are you completely stuck or have you tried something?

Answer 2

first thing you need to try is to find the anti derivative of the integrand

Answer 3

Well, for both scenarios there, I was taught to change the infinite interval/limit or infinite discontinuity into a limit by making the "infinite" part a variable. However, I have yet to figure out how to actually do the integral which is what satelite73 is advising.

Answer 4

yes you have to do that, but you have to find the anti derivative as well otherwise you cannot compute the limit

Answer 5

I see. Let me try to solve it.

Answer 6

lets take for granted that we have the anti derivative of ...ok i be quiet

Answer 7

u substitution?

Answer 8

Let t be a real number.\[\int\limits_{0}^{\infty} (1/(\sqrt{x}(x+1)))dx = \lim_{t \rightarrow 0}\int\limits_{t}^{1}(1/(\sqrt{x}(x+1)))dx + \lim_{t \rightarrow \infty}\int\limits_{1}^{t}(1/(\sqrt{x}(x+1)))dx\]right? Try u = sqrt(x) and remember the integrals of reverse trig. functions.

Answer 9

The answer is quite pretty :-)

Answer 10

lol! quite pretty? I gotta see this. thanks for the tip. Let's see if I can work it out.

Answer 11

Hmm I get pi/4 but my calculator says pi

Answer 12

I got pi also. Maybe some error in the limit calculation?

Answer 13

Perhaps, but thank you :) I'll just look over my work. I may have overlooked something.

Answer 14

No problem, mate. Pretty, eh?