Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its centroid at the point (1, 2, 3). The surface integral \int _{A}F^{\to}.dA^{\to} of a vector field F^{\to} = 3xi^{\^} + 5yj^{\^} + 6zk^{\^} over the entire surface A of the cube is ______.

GATE Mechanical Engineering (ME) 2022 Shift 2 Solved Paper

Question : 12 of 65

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Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its centroid at the point (1, 2, 3). The surface integral

∫ _{A}F↖{→}.dA↖{→}

of a vector field

F↖{→} = 3xi↖{\^} + 5yj↖{\^} + 6zk↖{\^}

over the entire surface A of the cube is ______.

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