Classical Dynamics of Particles and Systems · Problem 1-38

Newtonian Mechanics—Single Particle — Marion & Thornton

Physics — Mechanics · surface-integrals-stokes-theorem

Problem

Find the value of the integral

\int_S (\nabla \times \mathbf{A}) \cdot d\mathbf{a}

if the vector

\mathbf{A} = y\mathbf{i} + z\mathbf{j} + x\mathbf{k}

and

S

is the surface defined by the paraboloid

z = 1 - x^2 - y^2

, where

z \geq 0