How to calculate length and area for this curve?

Question

$C : x^{2/3} + y^{2/3} = 1$

I'm stuck, so any tip will be helpful

Thanks in advance!

Answer 1

The solution for $y$ is $$y(x) = (1 - x^{2/3})^{3/2}$$

The area $A$ is given by

$$A=4\int_0^1 y(x) dx=\frac{3\pi}{8}$$

The length $L$ of the curve is given by:

$$ L=4\int_0^1dx\sqrt{(y'(x))^2+1}=6$$