Answer
$\dfrac{40 \sqrt 5}{3}$
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:
$\int_C (x^2+y^2) ds=\int_0^2 [t^2+(2t^2))(\sqrt 5) dt\\=5 \sqrt 5 \int_0^{2} (t^2) dt\\=5\sqrt 5[\dfrac{t^3}{3}]_0^{2}\\=\dfrac{40 \sqrt 5}{3}$
