1. ## 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

2. ## 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 $\displaystyle f(x)=y^2(x)$, $\displaystyle g(x)=y(x)$

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

3. ## Re: Integration problem

I'm sorry but I don't get it, can you elaborate a little more?

4. ## 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 $\displaystyle x$?

5. ## 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

6. ## 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

7. ## Re: Integration problem

I get it! Clever way of solving the problem