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yrelhan4
 2 years ago
(1  x^3)^n integration. limits 0 to 1 ??
yrelhan4
 2 years ago
(1  x^3)^n integration. limits 0 to 1 ??

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experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0try trig sub x^3 = sin^2u

yrelhan4
 2 years ago
Best ResponseYou've already chosen the best response.0hmm.. i'll try it once and get back to you..

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2if that doesn't work, do u= 1x^3

yrelhan4
 2 years ago
Best ResponseYou've already chosen the best response.0how ould that help? @hartnn

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2du = 3x^2 dx du =  3(1u)^(2/3)dx du/[ 3(1u)^(2/3)] = dx just trying.......

timo86m
 2 years ago
Best ResponseYou've already chosen the best response.0intigrate with respect to x or n?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1356588801737:dw

timo86m
 2 years ago
Best ResponseYou've already chosen the best response.0x^3/ln(1x^3) With respect to n

yrelhan4
 2 years ago
Best ResponseYou've already chosen the best response.0@experimentX yes i did the same. i think i got it now.. thank you..

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0this should end up around beta function http://en.wikipedia.org/wiki/Beta_function#Properties

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2is this from Gamma Function ?

timo86m
 2 years ago
Best ResponseYou've already chosen the best response.0\[2/9\,{\frac {\Gamma \left( n+1 \right) \pi \,\sqrt {3}}{\Gamma \left( 2/3 \right) \Gamma \left( n+4/3 \right) }} \] gamma

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2because it gets the form u^n (1u)^n

timo86m
 2 years ago
Best ResponseYou've already chosen the best response.0oh and i used maple got no idea how to do it :P

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2http://www.wolframalpha.com/input/?i=integrate+%281x%5E3%29%5En+dx+from+0+to+1

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0\[ \frac{1}{3} \beta(2(n+1), 4/3)) = \]

wio
 2 years ago
Best ResponseYou've already chosen the best response.0Umm, can binomial theorem help with this?

wio
 2 years ago
Best ResponseYou've already chosen the best response.0\[ \Large (a+b)^n = \sum_{k=0}^{n}\binom{n}{k}a^{nk}b^{k} \]We let \(a = 1\) and \(b = x^3\)?

yrelhan4
 2 years ago
Best ResponseYou've already chosen the best response.0can anybody integrate 2/3 [(1t^2) / (t)^1/3] dt.. from 0 to 1.. i reached till here..

wio
 2 years ago
Best ResponseYou've already chosen the best response.0Like what about:\[ \Large \int_0^1\sum_{k=0}^{n}\binom{n}{k}(x^3)^{k}dx \]

yrelhan4
 2 years ago
Best ResponseYou've already chosen the best response.0@wio no idea about it.. its a grade 12 level question.. lol..

yrelhan4
 2 years ago
Best ResponseYou've already chosen the best response.0@experimentX 's method..

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0that's a good strategy!!

timo86m
 2 years ago
Best ResponseYou've already chosen the best response.0infinity to 2/3 [(1t^2) / (t)^1/3]

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2i don't think this can be solved without beta functions, did u go to wiki link of beta function ?

yrelhan4
 2 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=integrate+%5B%281t%5E2%29+%2F+%28t%29%5E1%2F3%5D+dt+from+0+to+1 i am talking about this..

yrelhan4
 2 years ago
Best ResponseYou've already chosen the best response.0@hartnn hmm.. i gotta read beta function once..

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=integrate+%5B%281t%5E2%29+%2F+%28t%29%5E1%2F3%5D+dt

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2thats easy to integrate just seperate the denominator.

yrelhan4
 2 years ago
Best ResponseYou've already chosen the best response.0i missed the n.. i think i gota read the beta/gamma function once.. thank you everyone..

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2yup, whether u put, u=1x^3 or x^3 = sin^2 u you'll end up with one of the form of beta function.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0for the last one \[ \frac 1 3 \times 2 \int_0^{\pi \over 2} \cos^{2(n+1)  1}(x) \sin ^{\frac 4 3  1 }(x) dx = \frac 13 \beta (n+1, \frac 23 ) = \frac 13 \frac{\Gamma(n+1) \Gamma(2/3)}{\Gamma(n+4/3) } \]

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0something went wrong
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