Using Either Stokes' Theorem or the Divergence Theorem (Whichever Is $\mathrm { Q } ( - 4 x \vec { i } + 3 y \vec { j } + 3 z \vec { k } ) \times \vec { d r }$

Short Answer

Using either Stokes' theorem or the Divergence theorem (whichever is appropriate), evaluate the following: $\mathrm { Q } ( - 4 x \vec { i } + 3 y \vec { j } + 3 z \vec { k } ) \times \vec { d r }$ where C is a closed loop parameterized by $\vec { r } ( t ) = ( \cos t + \sin t ) \vec { i } + \cos ^ { 3 } t \vec { j } + \sin ^ { 4 } t \vec { k }$