Answer
$18.6833$
Work Step by Step
Length of the curve can be obtained by using formula, such as
$L=\int_a^b |r'(t)| dt$
Now, $r'(t)=\lt 2t,3t^2,4t^3\gt$ ;$|r'(t)|=\sqrt {( 2t)^2+(3t^2)^2+(4t^3)^2}dt$
or, $=\sqrt{ 4t^2+9t^4+16t^6}$
Since, $L=\int_{0}^2(\sqrt{ 4t^2+9t^4+16t^6}) dt= 18.6833$
The above result is calculated with the help of a calculator.
