# How do you find the length of the curve #y=sqrt(x-x^2)#?

##### 1 Answer

Apr 26, 2016

Use algebra to get a length of

#### Explanation:

This is equivalent to (

This is the equation of a circle. Complete the square to get

With

The length of the upper semicircle is half the circumference.

**Note**

I also tried to do this using the integral, but it became too complicated for me to continue when there was a much cleaner solution available.