A difficult question
can anyone find the length of the following curve?
x^(2/3)+y^(2/3) =1

Question

A difficult question
can anyone find the length of the following curve?
x^(2/3)+y^(2/3) =1

anonymous · Answer

http://www.wolframalpha.com/input/?i=x%5E%282%2F3%29%2By%5E%282%2F3%29+%3D1+

anonymous · Answer

need to do it manually.

anonymous · Answer

First solve for y.
$$y ^{2/3}=1-x ^{2/3}$$
Cube both sides
$$y ^{2}=1-x ^{2}$$
$$y=\sqrt{1-x ^{2}}$$

anonymous · Answer

Then use arc length formula
$$\int\limits_{a}^{b}1+y ^{'2}$$

anonymous · Answer

good idea. But I'm afraid your cube is not correct. (1-x^(2/3))^3 doenst give you (1-x^(2))

anonymous · Answer

actually. we can do this by symmetry. find out one part of the curve first.  yes. find out y and then dy/dx first. after that we can use the length formula.

anonymous · Answer

yea.
$$y=\sqrt{1-x ^{2/3}}(1-x ^{2/3})$$

anonymous · Answer

did you get 3 as your final answer?

anonymous · Answer

What are your limits?

anonymous · Answer

0 to 1?

anonymous · Answer

bounded by  1 and 0. solve the length of the curve x belongs to (0,1) first.

anonymous · Answer

then times 2. symmetry

anonymous · Answer

Yea the integration gives you 3

anonymous · Answer

thanks!

anonymous · Answer

no prob