Integration problem

• Apr 3rd 2013, 12:54 AM
akhattab
Integration problem
I am trying to integrate y.(dy/dx) wrt x

I know the answer is (y^2)/2 but I don't know how to get the answer. Can someone please point me in the right direction
• Apr 3rd 2013, 01:13 AM
Ruun
Re: Integration problem
Is anything else than the chain rule:

$\displaystyle \frac{d}{dx}f(g(x))=\frac{df}{dg}\frac{dg}{dx}$

In your particular case $\displaystyle f(x)=y^2(x)$, $\displaystyle g(x)=y(x)$

$\displaystyle \frac{d}{dx}y^2=2y\frac{dy}{dx}$
• Apr 3rd 2013, 01:50 AM
akhattab
Re: Integration problem
I'm sorry but I don't get it, can you elaborate a little more?
• Apr 3rd 2013, 01:53 AM
Ruun
Re: Integration problem
Let $\displaystyle y(x)$ be any (differentiable) function of $\displaystyle x$. Do you know the derivative of $\displaystyle y^2(x)$ with respect to $\displaystyle x$?
• Apr 3rd 2013, 02:52 AM
akhattab
Re: Integration problem
Of course, 2y.(dy/dx)

But I don't get how that relates to my specific problem. I appreciate your patience with me :)
• Apr 3rd 2013, 02:57 AM
Ruun
Re: Integration problem
You have the following equality

$\displaystyle \frac{d}{dx}y^2(x)=2y\frac{dy}{dx}$

If two things are the same, their integrals should also be the same. So, integrate both sides and see what happens to the left hand side of the equation
• Apr 3rd 2013, 04:04 AM
akhattab
Re: Integration problem
I get it! Clever way of solving the problem :)