prove it (2 Viewers)

shuning · Jun 25, 2009

if $In=\int_{0}^{1}x(1-x)^ndx$
show that $In=\frac{n}{n+2}I_{n-1}$
hence show that $In=\frac{1}{2\cdot ^{n+2}C_{2}}$

n = 1,2,3 ........

HscGoldStarHero · Jun 25, 2009

ur a maths nerd haha

samthebear · Jun 25, 2009

HscGoldStarHero said:
ur a maths nerd haha

thats what you get for trolling in the ext 2 maths forum you turd.

hi shuning! havent seen you around for ages, thought u died or something XD

shuning · Jun 25, 2009

回复: Re: prove it

samthebear said:
thats what you get for trolling in the ext 2 maths forum you turd.

hi shuning! havent seen you around for ages, thought u died or something XD

xD hi

been busy with other stuff. just came back from the physic camp LOL.
btw how's ur life going? ^^

2replies... i thought some1 solved it for me LOL.

samthebear · Jun 25, 2009

Re: 回复: Re: prove it

shuning said:
xD hi

been busy with other stuff. just came back from the physic camp LOL.
btw how's ur life going? ^^

2replies... i thought some1 solved it for me LOL.

shame. one was a troll and the other... is going off-topic. i'd help you if i could but i dont do ext 2 =D
had fun at the physics camp? my classmate from chinese school went to the physics camp like 2 months (or somthing like that) ago and she was super excited over it. *sigh* only azn nerds. jksjks XD
and as you can see my life is sooo exciting that i find a compelling urge to spend most of my evening on BOS -repping trolls and verbally abusing them too.
chinese speaking trials on sat and i havent memorised anything =.= fun.

shuning · Jun 25, 2009

回复: Re: 回复: Re: prove it

the only good thing about the physics camp was that i got to hang around with friends.... apart from that... it's boring... i swear... the school is trying to make money that's y they hired the worst cabin's ever! once u entered it, u smell stinky socks everywhere.... u look under the bed... it's all stinky socks... ( god knows how long they've been down there.... )

lol chinese..... i wish i was doing cont too >.< oh well but i decided to do asain studies in uni where i major chinese again

bashing trolls arent a bad thing to kill time with... except half of the time i got bashed by em instead >.<

samthebear · Jun 25, 2009

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shuning said:
the only good thing about the physics camp was that i got to hang around with friends.... apart from that... it's boring... i swear... the school is trying to make money that's y they hired the worst cabin's ever! once u entered it, u smell stinky socks everywhere.... u look under the bed... it's all stinky socks... ( god knows how long they've been down there.... )

lol chinese..... i wish i was doing cont too >.< oh well but i decided to do asain studies in uni where i major chinese again

lol dont you do backgrounds? and yes schools are really just trying to make money out of you XD didnt you get to do anything exciting at the camp? like expriments and crap? or did they just do lectures? if they did then thats really dodgy (not to mention a waste of money)

shuning · Jun 25, 2009

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i dropped backgrounds ages ago LOL. too hard for me.... im only good enough for ext chinese xD

it's astrophys... we just travelled around look @ different telescopes and ppl talk to us about them. then we climbed the warnbundgle (sry wrong spelling but it's central NSW around Dubbo and Orange ) mountains ( 11km took 4 hrs LOL ), 3 ppl are dumb enough to get lost and ended up on top of another peak xD.

GUSSSSSSSSSSSSS · Jun 25, 2009

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lol shuning i got ur message (on my phone AND facebook xD)

i'll do it tonite and give it to u tomorrow ... thats if u have tutor tomorow arvo cos i'll probably be passing through or going to hornsby xD

goooooooooooooooooooooood conversation above btw =P cbb reading it tho lol

samthebear · Jun 25, 2009

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shuning said:
i dropped backgrounds ages ago LOL. too hard for me.... im only good enough for ext chinese xD

it's astrophys... we just travelled around look @ different telescopes and ppl talk to us about them. then we climbed the warnbundgle (sry wrong spelling but it's central NSW around Dubbo and Orange ) mountains ( 11km took 4 hrs LOL ), 3 ppl are dumb enough to get lost and ended up on top of another peak xD.

climbing a mountain. fun lol.

Hi GUSSSSSSSSSSSSS

shuning · Jun 25, 2009

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but i hate the bus trip.... we r pretty much on bus 24/7 then listen to lectures... cuz it's astro and we looking @ the stars.... so pretty much during the day we go 2 big observertoies ( cuz we cant use the telescope there) and they give us lecture. and @ night we watch the stars from other small observertories and they give us lecture again!!!! and the lecture r pretty much repeated everywhere.....

to get home... 7hrs bus + 1.5hr train... >.<

samthebear · Jun 25, 2009

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shuning said:
but i hate the bus trip.... we r pretty much on bus 24/7 then listen to lectures... cuz it's astro and we looking @ the stars.... so pretty much during the day we go 2 big observertoies ( cuz we cant use the telescope there) and they give us lecture. and @ night we watch the stars from other small observertories and they give us lecture again!!!! and the lecture r pretty much repeated everywhere.....

to get home... 7hrs bus + 1.5hr train... >.<

wow. i sympathise. the time it took you to get home from that place is about how long it takes to fly to another country haha. but i reckon the lectures would be shitter =/ at least you got to look at stars?

shuning · Jun 25, 2009

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yea... but pretty much with a naked eye the star looks like a dot. with a telescope the star looks like a BIGGGER dot twice the radius and comes with a few lil dots around it LOL... >.<

jet · Jun 25, 2009

Sounds like cosmology. Did you go around coonabarabran?

shuning · Jun 25, 2009

回复: Re: prove it

jetblack2007 said:
Sounds like cosmology. Did you go around coonabarabran?

yea we did xD

P.S when i saw ur name i thought u came in and saved the day LOL.... but the Q is still not solved T.T

jet · Jun 25, 2009

Lol. I can see the second bit really easily. Its the reduction im working on

shuning · Jun 25, 2009

回复: Re: prove it

i only need the 1st bit now.... cuz i just realized i havent done binominal theorem yet xD

samthebear · Jun 25, 2009

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shuning said:
yea... but pretty much with a naked eye the star looks like a dot. with a telescope the star looks like a BIGGGER dot twice the radius and comes with a few lil dots around it LOL... >.<

shame 'bout that >.< but at least you got to see a BIGGER dot with lil dots around it haha =P
i'm amazed no one has answered your question yet considering how much this conversation is bumping the thread to the top.

annabackwards · Jun 25, 2009

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Welcome back, Shuning!

I'd also like to commend everyone in this post as they have obviously attempted to answer the original question

By the way, just use integration by parts and rearrange to prove that equation. I can't be bothered enough to show you the actual working out XD

jet · Jun 25, 2009

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Got it.
$I_n = \int^1_0 x\left(1-x \right )^n \, dx \\ \text{let } u = \left( 1 - x \right )^{n}, du = -n\left(1 - x \right )^{n-1} \, dx \\ dv = x \, dx, v = \frac{x^2}{2} \\ \therefore I_n = \left [\frac{x^2 \left(1 - x \right )^n}{2} \right ] + \frac{n}{2} \int^1_0 x^2 \left(1 - x\right )^{n-1} \, dx I_n = \frac{n}{2} \int^1_0 x^2 \left (1 - x \right )^{n - 1} \, dx \\ 2I_n = -n\int^1_0 \left(x - x^2 - x \right )(1 - x)^{n-1} \, dx \\ = -n \int^1_0 x(1 - x)^n - x(1 - x)^{n-1} \, dx \\ = nI_{n - 1} - nI_n \\ (n + 2)I_n = nI_{n-1} \\ I_n = \frac{n}{n+1}I_{n-1}$

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