Arc Length (calculus) help?

Question

I'm having an issue starting up this problem

y^2= 4(x+4)^3 , 0<or= x <or= 2 , y>0

Can anyone help me?

Answer 1

The equation is y² = 4(x + 4)³.

y =  √ [4(x + 4)³] 

Therefore f(x) =  2(x + 4)^3/2

Apply derivative to each side.

f'(x) = 2(3/2) (x + 4)^{3/2 - 1}

= 3(x + 4)^(3-2)/2

= 3(x + 4)^1/2

Arc length L can be found by using the formula:

Therefore arc length is 13.54 units.