- #1

Hawkingo

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## Homework Statement

If ##\vec { F } = x \hat { i } + y \hat { j } + z \hat { k }## then find the value of ##\int \int _ { S } \vec { F } \cdot \hat { n } d s## where S is the sphere ##x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4##.

## The Attempt at a Solution

From gauss divergence theorem we know

##\int \int _ { S } \vec { F } \cdot \hat { n } d s = \int \int \int _ { V } \vec { \nabla } \cdot \vec { F } d v##

So ##\int \int _ { S } \vec { F } \cdot \hat { n } d s = \int \int \int _ { V } [ \frac { \partial } { \partial x } ( x ) + \frac { \partial } { \partial y } ( y ) + \frac { \partial } { \partial z } ( z ) ] d x d y d z##

=##3 \int \int \int _ { V } d x d y d z##

Here if I'll calculate the answer using gauss divergence theorem, then I have to find the volume integral of the function, but how will I take the limits of the integration. Can someone help please?

Thank you.

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