Question

What is the arclength of `f(x)=(1-x^(2/3))^(3/2)` in the interval `[0,1]`?

Answer 1

`3/2`

Explanation:

We get
`f'(x)=-sqrt(1-x^(2/3))/x^(1/3)`
and we have to solve
`int_0^1sqrt(1+(1-x^(2/3))/x^(2/3))dx`
simplifying the Integrand we get
`int_0^1x^(-1/3)dx=[3/2x^(2/3)]_0^1=3/2`