- #1

member 428835

## Homework Statement

Find the externals of the functional

$$\int\sqrt{x^2+y^2}\sqrt{1+y'^2}\,dx$$

Hint: use polar coordinates.

## Homework Equations

##x=r\cos\theta##

##y=r\sin\theta##

## The Attempt at a Solution

Transforming the given functional where ##r=r(\theta)## yields

$$\int r\sqrt{1+\left(\frac{r'(\theta)\sin\theta+r\cos\theta}{r'(\theta)\cos\theta-r\sin\theta}\right)^2}(r'(\theta)\cos\theta-r\sin\theta)\,d\theta$$ which doesn't seem to help much. Does anyone see anyhting I did wrong?