Let $\left. \vec { F } = \left( e ^ { y } + 5 x \right) \right) \vec { i } + \left( 4 y + z \cos x ^ { 5 } \right) \vec { j } + ( 2 z + 5 x ) \vec { k }$ Calculate the flux $\int _ { S } \vec { F } \cdot \vec { d A }$ , where S is the sphere (x-2)² + (y-3)² + z² = $4$ oriented inward.

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The Answer of Let $\left. \vec { F } = \left( e ^ { y } + 5 x \right) \right) \vec { i } + \left( 4 y + z \cos x ^ { 5 } \right) \vec { j } + ( 2 z + 5 x ) \vec { k }$ Calculate the flux $\int _ { S } \vec { F } \cdot \vec { d A }$ , where S is the sphere (x-2)² + (y-3)² + z² = $4$ oriented inward.

Let F⃗=(ey+5x))i⃗+(4y+zcos⁡x5)j⃗+(2z+5x)k⃗\left. \vec { F } = \left( e ^ { y } + 5 x \right) \right) \vec { i } + \left( 4 y + z \cos x ^ { 5 } \right) \vec { j } + ( 2 z + 5 x ) \vec { k }F=(ey+5x))i+(4y+zcosx5)j​+(2z+5x)k

Let $\left. \vec { F } = \left( e ^ { y } + 5 x \right) \right) \vec { i } + \left( 4 y + z \cos x ^ { 5 } \right) \vec { j } + ( 2 z + 5 x ) \vec { k }$