* A vector is defined as $\to f = y^i + x^j + z^k$ where $^i^j$ and $^k$ are unit vectors in Cartesian (x, y, z) coordinate system. The surface integral $∯$ f. ds over the closed surface S of a cube with vertices having the following coordinates;
(0,0,0). (1,0,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1), (1,1,0) is______
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Solution

The correct option is A 1
div $\to f = \frac{\partial}{\partial x} (y) + \frac{\partial}{\partial y} (x) + \frac{\partial}{\partial z} (z) = 1$
By Gauss-divergence theorem
$∯$ $\to f . \to s = \int_{0}^{1} \int_{0}^{1} \int_{0}^{1} d i v \to f d v$ $= \int_{0}^{1} \int_{0}^{1} \int_{0}^{1} 1 d x d y d z$
=V
=Volume of the unit cube=1

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