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Find the arc length of x^(2 / 3) + y^( 2 / 3) = 1.

Question:

Find the arc length of {eq}\displaystyle x^\frac {2}{3} + y^\frac{2}{3} = 1 {/eq}.

Arc Length:

Arc length of the curve y = f(x) is given by

{eq}L = 4 \int_0^1 \sqrt{1+f'(x)^2} dx {/eq}

Answer and Explanation:

Given {eq}x^{\frac23} + y^{\frac23} = 1 {/eq}

Arc length is given by

{eq}L = 4 \int_0^1 \sqrt{1+f'(x)^2} dx \\ y = f(x) =...

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Arc Length of a Sector: Definition and Area

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