Arc length of a curve

MediumCalculus~4m

Find the arc length of the curve $y = \tfrac{2}{3}x^{3/2}$ from $x=0$ to $x=3$ . (to 3 decimals)

Show hints (2)+

$L=\int_a^b\sqrt{1+(y')^2}\,dx$ ; here $y'=\sqrt x$ so the radical becomes $\sqrt{1+x}$ .
Antiderivative $\tfrac23(1+x)^{3/2}$ ; note $4^{3/2}=8$ .

Answer

Reveal answer →

4.667 (± 0.005)

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