用第二类曲面积分求xdydz+ydzdx+zdxdy

问题描述:

用第二类曲面积分求xdydz+ydzdx+zdxdy
积分曲面为球面x^2+Y^2+Z^2=A^2的外侧

xdydz+ydzdx+zdxdy
=3×2∫∫zdxdy
=6∫∫ 根号下(A²-x²-y²)dxdy
=6∫2π 0∫A,0 根号下(A²-r²)rdr
=4πA³