improper substition?

Bazman · **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?

Shadow · **Posted:** Mon, 16 Apr 2012 14:28:18 UTC

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.

Bazman · **Joined:** Mon, 29 Jan 2007 13:48:38 UTC **Posts:** 537

Thanks

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improper substition?

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