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 Post subject: improper substition?
PostPosted: Mon, 16 Apr 2012 14:01:17 UTC 
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Joined: Mon, 29 Jan 2007 13:48:38 UTC
Posts: 537
Hi there,

I have to intergate

\int_0^1 x^2 (1-x^2)^{n-1} dx

to deal with the second term I use the substitution

u=1-x^2

so

\int _1^ 0 -\frac{(1-u)^{0.5} u^{n-1}}{2} du

which I then apply integration by parts to with

u'=u^{n-1} u=\frac{u^n}{n}

v=(1-u)^{0.5}   v'=-0.5(1-u)^{0.5}

[\frac{u^n(1-u)^0.5}{2n}]_1^0=0

\int_1^0 \frac{-(1-u)^{0.5} u^n}{4n}}

Is this correct so far?


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 Post subject: Re: improper substition?
PostPosted: Mon, 16 Apr 2012 14:28:18 UTC 
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12170
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Bazman wrote:
Hi there,

I have to intergate

\int_0^1 x^2 (1-x^2)^{n-1} dx

to deal with the second term I use the substitution

u=1-x^2

so

\int _1^ 0 -\frac{(1-u)^{0.5} u^{n-1}}{2} du

which I then apply integration by parts to with

u'=u^{n-1} u=\frac{u^n}{n}

v=(1-u)^{0.5}   v'=-0.5(1-u)^{0.5}

[\frac{u^n(1-u)^0.5}{2n}]_1^0=0

\int_1^0 \frac{-(1-u)^{0.5} u^n}{4n}}

Is this correct so far?


Your v' is wrong.

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 Post subject: Re: improper substition?
PostPosted: Tue, 17 Apr 2012 17:41:13 UTC 
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Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 29 Jan 2007 13:48:38 UTC
Posts: 537
Thanks


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