jchapman jchapman

01-02-2017
Mathematics

Answered

Find the length of the curve y=3x^3/2 from x=0 to x=5/9

Verified Answer :

LammettHash LammettHash

07-02-2017

\(y=3x^{3/2}\implies y'=\dfrac92x^{1/2}\)

The length of the curve is

\(L=\displaystyle\int_0^{5/9}\sqrt{1+\left(\dfrac92x^{1/2}\right)^2}\,\mathrm dx=\int_0^{5/9}\sqrt{1+\dfrac{81}4x}\,\mathrm dx=\dfrac{335}{243}\)

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