we are given
[tex]r(t)=(7t,3cos(t),3sin(t))[/tex]
we can find x , y and z
[tex]x=7t,y=3cos(t),z=3sin(t))[/tex]
now, we can use arc length formula
[tex]L=\int\limits^a_b {\sqrt{(x')^2+(y')^2+(z')^2} } \, dt[/tex]
now, we can find derivative
[tex]x'=7,y'=-3sin(t),z'=3cos(t))[/tex]
now, we can plug values
and we get
[tex]L=\int _{-2}^2\sqrt{7^2+\left(-3\sin \left(t\right)\right)^2+\left(3\cos \left(t\right)\right)^2}dt[/tex]
[tex]L=\int _{-2}^2\sqrt{7^2+9}dt[/tex]
[tex]=\sqrt{58}\cdot \:2-\left(-2\sqrt{58}\right)[/tex]
[tex]L=4\sqrt{58}[/tex]...........Answer
