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## Homework Statement

find the values of the integral

[itex] \int_{S} \vec A\cdot\ d\vec a [/itex]

where,

[itex] \vec A\ = (x^2+y^2+z^2)(x\hat e_{1}+y\hat e_{2}+z\hat e_{3}) [/itex]

and the surface S is defined by the sphere [itex] R^2=x^2+y^2+z^2 [/itex]

## Homework Equations

first i must evaluate the integral directly, so i don't think there are any specific formulas other than ones you must derive from the geometry specific to the problem. i also have to calculate using gauss' theorem but for that there's a simple equation.

## The Attempt at a Solution

really looking for an explanation on surface integrals. i know that [itex] d\vec a [/itex] is a small area on the surface of the sphere and equations must be derived from the geometry. im having a hard time visualizing this and how it's suppose to work. for now, i would appreciate a good explanation of surface integrals to help me visualize the problem.

thanks in advance.