Hi.

I'm having lots of trouble with the integration of arccos if someone can help. Here is the question.

integral (arccos(root x))^2 dx. or equivalently:

integral (arccos(x^1/2))^2

I'm not sure where to start. Or what substitution I should make.

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- Feb 28th 2011, 06:41 AMKumaHow to integrate arccos?
Hi.

I'm having lots of trouble with the integration of arccos if someone can help. Here is the question.

integral (arccos(root x))^2 dx. or equivalently:

integral (arccos(x^1/2))^2

I'm not sure where to start. Or what substitution I should make. - Feb 28th 2011, 07:38 AMe^(i*pi)
$\displaystyle u = \arccos(\sqrt{x}) \implies x = \cos^2 u$

$\displaystyle dx = -2\sin u \cos u du$

$\displaystyle \displaystyle \int \arccos(\sqrt{x})\, dx = \int u \cdot -\sin(2u) du$

Use integration by parts