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

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

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Answer 1 · 2018-06-06T13:05:31

#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#

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

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