Question

determine if the integral is convergent or divergent
\[\int\limits_{0}^{\infty} 1/\sqrt{x+1}\]

Answer 1

looks like diverges.

Answer 2

probably, yeah
but how to show it...

Answer 3

i don't know hot to show it.

Answer 4

oh I know, comparison

Answer 5

ask wolf bro first
http://www.wolframalpha.com/input/?i=integrate+from+0+to+infinity+1%2Fsqrt%281%2Bx%29

Answer 6

i need to learn these for my test so i can't depend on wolfram

Answer 7

ways to show it :)

Answer 8

integrate it --> that will give infinity.

Answer 9

oh yeah, duh... :P

Answer 10

also summation of 1/sqrt(x+1) <--- itself seems to diverge <-- by ratio test.

Answer 11

@TuringTest done something like this before??
http://openstudy.com/study#/updates/4f883247e4b0505bf08753ec

Answer 12

i'm so confused.

Answer 13

i'll try to integrate it now.

Answer 14

http://en.wikipedia.org/wiki/Integral_test_for_convergence

Answer 15

2\[2\sqrt{\infty+1}-2\sqrt{0+1}\]

Answer 16

in general for indefinite integrals we want to write\[\int_{0}^{n}\frac1{\sqrt{1+x}}dx\]then take the limit as \(n\to\infty\)

Answer 17

@azalea that's a very unconventional way to write it. Your teacher may not like that.

Answer 18

also it's not quite right...

Answer 19

LOL. oh ok

Answer 20

I thought you were doing integral test for convergence of 1/sqrt(1+x)

Answer 21

try what I said\[\int_{0}^{n}\frac1{\sqrt{1+x}}dx\]then take the limit as n goes to infinity

Answer 22

I don't like it too.

Answer 23

yeah i did it wrong

Answer 24

\[\lim_{0 \rightarrow t}\int\limits_{0}^{t}1/\sqrt{(x+1)}\]

Answer 25

where t=infinity

Answer 26

dx missing.

Answer 27

not quite...
limit is wrong too

Answer 28

oh yeah. i forgot the dx.

Answer 29

\[\lim_{n\to\infty}\int_{0}^{n}\frac1{\sqrt{1+x}}dx\]

Answer 30

i meant t--> infinity

Answer 31

\[\lim_{t \rightarrow \infty}2\sqrt{(x+1)} \]

Answer 32

then as the limit approaches infinity it's infinity

Answer 33

you should have already plugged in the t, and you forgot the evaluation at 0, but yeah

Answer 34

oh yeah i didn' finish

Answer 35

\[2\sqrt{(t+1)}-2\sqrt{(0+1)}\]

Answer 36

yup, you got it :)

Answer 37

\[2\sqrt{(t+1)}-2\]

Answer 38

put the limit there.