求曲线ρ=asinx,ρ=a(cosx+sinx)(a>0)所围图形公共部分的面积(不画图如何解题?

Question

求曲线ρ=asinx,ρ=a(cosx+sinx)(a>0)所围图形公共部分的面积(不画图如何解题?

Answer 1

要画图,不画图不是好习惯.S=∫[0,π/2]dx∫[0,asinx]rdr+∫[π/2,3π/4]dx∫[0,a(cosx+sinx)]rdr  =a^2/2∫[0,π/2](sinx)^2dx+a^2/2∫[π/2,3π/4](cosx+sinx)^2dx  =πa^2/8+  a^2/2(1/4*pi-1/2)&n...