Answer
$80 \pi$
Work Step by Step
Since, we have $ds=\sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dt})^2+(\dfrac{dz}{dt})^2} dt$
or, $ds=\sqrt{(-4 \sin t)^2+( 4 \cos t )^2+(3)^2} dt \implies ds= \sqrt {25} dt=5 dt$
Now, the line integral is: $\int_C \sqrt{x^2+y^2} ds=\int_{-2 \pi}^{2 \pi} \sqrt {16 \cos ^2 t+16 \sin ^2 t} (5) dt$
or, $=20(4 \pi)$
or, $=80 \pi$
