So the formula is

My question is regarding the piecewise function.

I currently know the area of this function which is 12.8 and has a height of 8 and a base of 4. Using pythagorem theorem we get

So with that in mind I now go about finding the derivative of my function which is really just finding the first part of the equation.

Now putting back into the arc formula

Removing the 1 and putting it into the fraction gives me.

getting rid of the square root we have

If i have been correct thus far this is where things go a little bit hazzy and my answer doesn't look even remotely right.

Integrating I get approx 49.9 which is way above what I expected to get. Im expecting something close to why pythag gave me.

Maple suggests its roughly 9.6