How would you go about solving this one:

integral (y*sqrt(2-(2y)^2)) dy

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- Oct 19th 2013, 10:08 PMheatlyIntegral involving a surd .
How would you go about solving this one:

integral (y*sqrt(2-(2y)^2)) dy

- Oct 19th 2013, 10:16 PMSlipEternalRe: Integral involving a surd .
Try a u-substitution.

- Oct 19th 2013, 10:29 PMheatlyRe: Integral involving a surd .
I have tried that a couple of ways.

u=(2-(2y)^2) and also u=4y^2..........cant get it to work...what was your intended u sub. - Oct 19th 2013, 10:33 PMSlipEternalRe: Integral involving a surd .
$\displaystyle u = 2-(2y)^2$

$\displaystyle du = -4ydy$

$\displaystyle dy = \dfrac{du}{-4y}$

$\displaystyle \int y\sqrt{2-(2y)^2}dy = \int y\sqrt{u}\dfrac{du}{-4y} = -\dfrac{1}{4}\int u^{1/2}du$ - Oct 19th 2013, 10:34 PMProve ItRe: Integral involving a surd .
- Oct 19th 2013, 10:39 PMheatlyRe: Integral involving a surd .
Thanks a lot