Calculating Arc Length of a Polar Curve

[kira137]

Homework Statement

Find the length of the curve x^(2/3)+y^(2/3) = 1 for x in the interval [0.1].

The attempt at a solution

y = (1-x)^(2/3)
f'(x) = (4x^(-1/3) (1-x^(2/3))^(1/2))/9

then i plugged it into arc length formula
1
S sqrt(1+((4x^(-1/3) (1-x^(2/3))^(1/2))/9)^2 =
0

1
S sqrt(1+((16x^(-2/3) (1-x^(2/3))/81) =
0

1
S sqrt(1+((16x^(-2/3) -16)/81) =
0

1
S sqrt(16x^(-2/3) +65))/81 =
0

'''''''''1
1/9 S sqrt(16x^(-2/3) +65) = ...
'''''''''0

then I got stuck.. I wasn't even sure if I was solving this question the right way.
If I let u = (16x^(-2/3) +65), then whole bunch of weird numbers come out..

thank you in advance

 

[Bohrok]

You started with the wrong equation for y. Exponents are wrong or missing.