Answer
$\dfrac{2 \sqrt 2}{3}$
Work Step by Step
We 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:
$\int_C (x^2+y^2) ds=\int_0^1 (t^2+t^2)(\sqrt 2) dt\\=2\sqrt 2 \int_0^{1} t^2 dt\\=2\sqrt 2[\dfrac{t^3}{3}]_0^{1}\\=\dfrac{2 \sqrt 2}{3}$
