# What is the arc length of #f(x)=6x^(3/2)+1 # on #x in [5,7]#?

##### 1 Answer

Mar 19, 2018

#### Explanation:

#f(x)=6x^(3/2)+1#

#f'(x)=9sqrtx#

Arc length is given by:

#L=int_5^7sqrt(1+81x)dx#

Integrate directly:

#L=2/243[(1+81x)^(3/2)]_5^7#

Hence

#L=4/243(568sqrt142-203sqrt406)#