求大师赐教!r=a(1+sinθ)所围图形的面积.
1个回答
展开全部
面积=S_{θ:0->2PI}(1/2)r^2dθ=S_{θ:0->2PI}(1/2)a^2(1+sin(θ))^2dθ
=(1/2)a^2S_{θ:0->2PI}[1+2sin(θ) + (sin(θ))^2]dθ
=a^2/2S_{θ:0->2PI}[1+2sin(θ)]dθ + a^2/2S_{θ:0->2PI}[1-cos(2θ)]/2dθ
=a^2/2[θ - 2cos(θ)]_{θ:0->2PI} + a^2/4[θ - (1/2)sin(2θ)]_{θ:0->2PI}
=a^2/2[2PI-2+2] + a^2/4[2PI]
=(3PI/2)a^2
其中,PI=3.1415926
=(1/2)a^2S_{θ:0->2PI}[1+2sin(θ) + (sin(θ))^2]dθ
=a^2/2S_{θ:0->2PI}[1+2sin(θ)]dθ + a^2/2S_{θ:0->2PI}[1-cos(2θ)]/2dθ
=a^2/2[θ - 2cos(θ)]_{θ:0->2PI} + a^2/4[θ - (1/2)sin(2θ)]_{θ:0->2PI}
=a^2/2[2PI-2+2] + a^2/4[2PI]
=(3PI/2)a^2
其中,PI=3.1415926
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
