Let C be the circle in space with the parameterization $\vec { r } ( t ) = \cos t \vec { i } + \sin t \vec { k } , \quad 0 \leq t \leq 2 \pi$ Evaluate $\int_{C} \vec{F} \cdot d \vec{r}$ where $\vec { F } = 2 z e ^ { y ^ { 2 } } \vec { i } + \sin \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) \vec { j } + x \left( y ^ { 2 } - 1 \right) \vec { k }$

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The Answer of Let C be the circle in space with the parameterization $\vec { r } ( t ) = \cos t \vec { i } + \sin t \vec { k } , \quad 0 \leq t \leq 2 \pi$ Evaluate $\int_{C} \vec{F} \cdot d \vec{r}$ where $\vec { F } = 2 z e ^ { y ^ { 2 } } \vec { i } + \sin \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) \vec { j } + x \left( y ^ { 2 } - 1 \right) \vec { k }$

Let C Be the Circle in Space with the Parameterization r⃗(t)=cos⁡ti⃗+sin⁡tk⃗,0≤t≤2π\vec { r } ( t ) = \cos t \vec { i } + \sin t \vec { k } , \quad 0 \leq t \leq 2 \pir(t)=costi+sintk,0≤t≤2π

Let C Be the Circle in Space with the Parameterization $\vec { r } ( t ) = \cos t \vec { i } + \sin t \vec { k } , \quad 0 \leq t \leq 2 \pi$