高数题，二重积分求解，能写下过程吗，感谢 20
2个回答
展开全部
极坐标积分范围如图
已赞过
已踩过<
评论
收起
你对这个回答的评价是？
展开全部
I = ∫∫<D>(x^2+y^2)dxdy = ∫<-π/2, π/2>dt ∫<0, acost>r^2 rdr
= (1/4)∫<-π/2, π/2>dt [r^4]<0, acost>
= (a^4/4)∫<-π/2, π/2>(cost)^4dt = (a^4/16)∫<-π/2, π/2>(1+cos2t)^2dt
= (a^4/16)∫<-π/2, π/2>[1+2cos2t+(cos2t)^2]dt
= (a^4/16)∫<-π/2, π/2>[3/2+2cos2t+(1/2)cos4t]dt
= (a^4/16)[3t/2 + sin2t + (1/8)sin4t]<-π/2, π/2> = 3πa^4/32
= (1/4)∫<-π/2, π/2>dt [r^4]<0, acost>
= (a^4/4)∫<-π/2, π/2>(cost)^4dt = (a^4/16)∫<-π/2, π/2>(1+cos2t)^2dt
= (a^4/16)∫<-π/2, π/2>[1+2cos2t+(cos2t)^2]dt
= (a^4/16)∫<-π/2, π/2>[3/2+2cos2t+(1/2)cos4t]dt
= (a^4/16)[3t/2 + sin2t + (1/8)sin4t]<-π/2, π/2> = 3πa^4/32
本回答被网友采纳
已赞过
已踩过<
评论
收起
你对这个回答的评价是？
推荐律师服务：
若未解决您的问题，请您详细描述您的问题，通过百度律临进行免费专业咨询
