Classical Dynamics of Particles and Systems · Problem 1-37

Newtonian Mechanics—Single Particle — Marion & Thornton

Physics — Mechanics · surface-integrals-gauss-theorem

Problem

Find the value of the integral

\int_S \mathbf{A} \cdot d\mathbf{a}

, where

\mathbf{A} = (x^2 + y^2 + z^2)(x\mathbf{i} + y\mathbf{j} + z\mathbf{k})

and the surface

S

is defined by the sphere

R^2 = x^2 + y^2 + z^2

. Do the integral directly and also by using Gauss's theorem.