#### Answer

$0$

#### Work Step by Step

Given: $\int_C F \cdot T ds-\int_C F. dr=\int_C (x+y) dx +(x+y) dy$
Now,
$\int_C (x+y) dx +(x+y) dy=\int_C (x+y) dx + \int_C (x+y) dy$
and $\int_0^{2\pi}(2 \cos t +2\sin t) (-2 \sin t dt ) +(2 \cos t +2\sin t) (2 \cos t dt ) =\int_{0}^{2\pi} (4) (\cos 2t) dt=0$