Question

求助这题怎么做呀，求详细过程谢谢

Answer 1

根据格林定理

I=∫∫[d(2xy-x^2cosy+x)/dx - d(1-2xsiny +3x^2y^2)/dy] dx dy

=∫∫ 2y-2xcosy +1 +2xcosy +6x^2y)dxdy

=∫∫2y +6x^2y +1)dxdy

=∫∫2rsint +6r^3 (cos^2t sint)+1)rdtdr

=∫∫2r^2sint drdt +∫∫ 6r^4cos^2tsint drdt +∫∫ 6r^4drdt

前两个积分都是关于角度对称区间上的定积分，为0

=∫∫ 6r^4drdt = 2pi * 6/5 r^5|0, a

= 12pi/6 *a^5