前>>144
>>前スレ737
V_CL/2=π∫[t=0→√2/2]｛√2/2+√(1-t^2)｝^2dt
+2π∫[t=√2/2→1]√(1-t^2)dt
=π∫[θ=0→π/4]｛√2/2+cosθ｝^2cosθdθ
+2π∫[θ=π/4→π/2]cosθcosθdθ
=π∫[θ=0→π/4]｛1/2+cosθ√2+cos^2θ｝cosθdθ
+2π∫[θ=π/4→π/2](1/2+cos2θ/2)dθ
=π∫[θ=0→π/4](cosθ/2+cos^2θ√2+cos^3θ)dθ
+2π∫[θ=π/4→π/2](1/2+cos2θ/2)dθ
=π∫[θ=0→π/4](cosθ/2+√2/2+cos^2θ√2/2+cos3θ/4+3cosθ/4)dθ
+2π∫[θ=π/4→π/2](1/2+cos2θ/2)dθ
=π∫[θ=0→π/4](5cosθ/4+√2/2+cos2θ√2/2+cos3θ/4)dθ
+2π∫[θ=π/4→π/2](1/2+cos2θ/2)dθ
=π[θ=0→π/4][5sinθ/4+θ√2/2+sin2θ√2/4+sin3θ/12]
+2π∫[θ=π/4→π/2][θ/2sin2θ/4]
=π(5√2/8+π√2/8+√2/4+√2/24)+2π(π/4-π/8-1/4)
=π(5√2/8+π√2/8+7√2/24)+π(π/4-1/2)
=π(11√2/12+π√2/8+π/4-1/2)
=2.13712096284……π＞2π＞π
目測誤った。
大きすぎるということは、もっと中心はx軸に近い。