高数二重积分求大佬详细解答！！！详细！！！万分感谢

16. 积分域对称于 x 轴， y 的奇函数 2yx^3 积分是0.
I = ∫∫<D>x^2(x^2+y^2)dxdy 化极坐标
=  ∫<-π/2, π/2>dt∫<0, 2cost> r^2(cost)^2 r^2 rdr
=  ∫<-π/2, π/2>(cost)^2dt∫<0, 2cost> r^5dr
=  ∫<-π/2, π/2>(cost)^2dt[r^6/6]<0, 2cost>
= (32/3)∫<-π/2, π/2>(cost)^8dt = (64/3)∫<0, π/2>(cost)^8dt
= (64/3)(7/8)(5/6)(3/4)(1/2)(π/2) = 35π/12