Hello everyone!

I've lately been thinking about this: why isn't $\displaystyle dxdy$ equal to $\displaystyle rdrd\theta$.

Okay now, $\displaystyle x=r\cos\theta$ and $\displaystyle y=r\sin\theta$.

So using the derivative rule, we say that $\displaystyle dx=\cos\theta dr-r\sin\theta d\theta$ and that $\displaystyle dy=\sin\theta dr+r\cos\theta d\theta$...

But when we carry out $\displaystyle dxdy$ we get something very long...

How is that?

Thanks!