# Thread: Integral involving a surd .

1. ## Integral involving a surd .

How would you go about solving this one:
integral (y*sqrt(2-(2y)^2)) dy

2. ## Re: Integral involving a surd .

Try a u-substitution.

3. ## Re: 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.

4. ## Re: Integral involving a surd .

$u = 2-(2y)^2$

$du = -4ydy$

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

$\int y\sqrt{2-(2y)^2}dy = \int y\sqrt{u}\dfrac{du}{-4y} = -\dfrac{1}{4}\int u^{1/2}du$

5. ## Re: Integral involving a surd .

Originally Posted by heatly
How would you go about solving this one:
integral (y*sqrt(2-(2y)^2)) dy
I'd lean towards making the substitution \displaystyle \begin{align*} 2y = \sqrt{2}\sin{(\theta)} \implies dy = \frac{\sqrt{2}}{2}\cos{(\theta)}\,d\theta \end{align*}...

Thanks a lot