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Without using the Divergence Theorem Evaluate the surface integral $\iint\limits_{\sum} f \cdot d\sigma $ of $f(x,y,z) = xi+ yj + zk , \sum: $ boundary of the solid cube S= $\{(x,y,z) = 0\leq x,y,z \leq 1)\}$

My attempt:

Here we have to use the following definition of surface integral.

Note that there will be a different outward unit normal vector to each of the six faces of the cube.

My attempt:

Here we have to use the following definition of surface integral.

Note that there will be a different outward unit normal vector to each of the six faces of the cube.

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