Question

compute the length of the curve from 0<= x <=3 of the function y = 1/3(x^2 +2)^3/2

Answer 1

just grab a measuring tape :DD

Answer 2

arc length = \(\large \int_0^3 \sqrt{1 + (\frac{dy}{dx})^2} dx \)

Answer 3

find the derivative and plugin

Answer 4

\(\large y = \frac{1}{3}(x^2 +2)^{\frac{3}{2}}\)

\(\large \frac{dy}{dx} = ?\)

Answer 5

ok... here goes! sorry, I skipped it and got caught up in another.

Answer 6

yah

Answer 7

\[\frac{ dy }{ dx }= (\frac{ 1 }{ 3 })(\frac{ 3 }{ 2 })(x^2+2)^{1/2}(2x) = \frac{ 1 }{ 2}(2x)(x^2+2)^{1/2}\]

Answer 8

well also the 1/2 cancels with the 2x

Answer 9

Looks good bro.
Plug it all in. Jam through it.