Answer
$\dfrac{5 \pi}{2}$
Work Step by Step
Need to compute the derivative for the parametric vector equation.
We need to re-write the line integral in terms of $t$ to simplify the integral by using parametric equations.
Now, the line integral is:
$\int_C 3(x^2+y^2+z^2) ds=\int_0^{\pi/2} (\sin^2 t+\cos^2 t+4) \sqrt {\cos^2 t +\sin^2t } dt\\=\int_0^{\pi/2} 5 \ dt \\=[5t]_0^{\pi/2}\\=\dfrac{5 \pi}{2}$
