int by parts

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April 19th 2010, 05:06 PM
WartonMorton

int by parts

Looking to integrate arcsin(x)*dx from 0 to 1 by method of int by parts. You get an improper integral when doing this, but want to do it regardless.
April 19th 2010, 05:10 PM
dwsmith

Quote:

Originally Posted by WartonMorton

Looking to integrate arcsin(x)*dx from 0 to 1 by method of int by parts. You get an improper integral when doing this, but want to do it regardless.

u=arcsin
dv=dx
April 19th 2010, 05:16 PM
WartonMorton

so du = 1/sqrt(1-x^2)
v=1

Can't quite put it all together.
April 19th 2010, 05:20 PM
dwsmith

$u=arcsinx$

$du=\frac{1}{\sqrt{-x^2}}dx$

$dv=dx$

$v=\int dx=x$

$uv-\int vdu$
April 19th 2010, 05:21 PM
harish21

Quote:

Originally Posted by WartonMorton

so du = 1/sqrt(1-x^2)
v=1

Can't quite put it all together.

$u = arcsinx \implies du = \frac{1}{\sqrt{1-x^2}} dx$

and,

$dv = dx \implies v = x$

using integration by parts, the expression is

$uv - \int v. \text{du}$

$= x \times arcsin(x) - \int \frac{x}{\sqrt{1-x^2}} dx$

Now for $\int \frac{x}{\sqrt{1-x^2}} dx$ , use substitution:

$u = 1-x^2$

and integrate

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