Question

is the imporer integral \[\int\limits\limits_{0}^{+\infty}re ^{-r ^{2}}dr\] convorgent? Justify your answer

Answer 1

i'm trying to solve it
but i am not soon to the answer yet -.-

Answer 2

lets take u=r^2 here will make the thing easier

Answer 3

now we have \[\int\limits_{0}^{+\infty}re^{-u}dr\]

Answer 4

and now i guess we can do that :
\[1/2 \int\limits_{0}^{+\infty}e ^{-u}du\]

Answer 5

k now we got \[(-1/2)e^{-r ^{2}} + c\]

Answer 6

there we go

Answer 7

making u=-r^2 would have been a little bit easier

Answer 8

\[\int\limits_{0}^{+\infty}re ^{-r ^{2}}dr = \lim_{l \rightarrow \infty}\int\limits_{0}^{1}re ^{-r ^{2}}dr\]

Answer 9

as r goes to infinity 1/r^2 goes to 0

Answer 10

now i think we can say \[\lim_{l \rightarrow \infty}1/2 [-e ^{-l ^{2}}]^l\]

Answer 11

yeapp

Answer 12

\[-\frac{1}{2}e^{\frac{1}{r^2}}\]

\[-\frac{1}{2}e^0\]

-1/2

Answer 13

and now lets work on it.... ok now we get -1/2[0-2] = 1/2

Answer 14

so the given integral converges to 1/2 i guess

Answer 15

yes 1/2

Answer 16

how old are you man? :D

Answer 17

why?

Answer 18

no reason :D there shuld not everything has a reson

Answer 19

19

Answer 20

me = 14

Answer 21

14 and already doing integral, nice!

Answer 22

yeap :D 3 mounths ago, i did not kno even limits, :D it took only three mounths me to learn algebra 1-2, calculus 1-2 :D not seeen a really hard stuff yet :(

Answer 23

doing calculus is not hard, applying it is somewhat difficult

Answer 24

yes :D exatly i sometimes need calculus in my 2D games, and it really beings hard to use the things i know -.-' really i always need to have a look at books ...

Answer 25

games, tell me about that

Answer 26

well, i begin to work on sof. dev. when i was 12, learned functions when i was 12 :D well i begin with QBASIC, solved over 6.000 algorithm quesitons learned, C, C++, C#, VB.GWBASIC, some java, PHP ... nowadays i work on Assembly X86 :D , i developed over 4 o 5 games in C#,XNA , wrote all the algorithms that i need in my game on my own (for example to make a cannon rotate :D ) nowadays i am trying to learn C++ with DirectX too :D to develop better games :D but i need to work calculus 3 much thrre dimensional space to start to work on 3D game programming :D :D thats why i just stopped to work on game programming much and started to work on maths last three mounths :D and learned limit, differential , contiunity, integral ... etc thousends of things in these threee mounths in 2 or 1 more mounths ill be able to start to work on three dimensional space, :D and in the mean time i learn about DirectX so ill contiune at where i stopped on game programming :D

Answer 27

and i think its the hardest question i ever solved : http://openstudy.com/groups/mathematics#/groups/mathematics/updates/4e6a40800b8b4a2b95d45a89