# Find the length of the specified arc of the given curve

gigi9
Calc help plz!!!

Plz help me out w/ the problem below. Thanks.
Find the length of the specified arc of the given curve:
y=1/3sqrt(x)*(3-x), 0<=x <=3
Formular to find arc length is integral from a to b of sqrt(1+f'(x)^2)dx
I got to these steps below and not sure exactly wat to do next
***y'=1/6x^(-1/2)(3-3x)=1/2x^(-1/2)(1-x)
***V= integral from 0 to 3 of sqrt{1+[1/2x^(-1/2)*(1-x)])2} dx
=integral 0 to 3 of sqrt[1/2+1/4*x^-1+1/4*x] dx

## Answers and Replies

KLscilevothma
V= integral from 0 to 3 of sqrt{1+[1/2x^(-1/2)*(1-x)])2} dx
=integral 0 to 3 of sqrt[1/2+1/4*x^-1+1/4*x] dx

1/(4x) + 1/2 + x/4 can be factorized to (1/2x-1/2 + 1/21/2)2