求由锥面z=k/R *√x²+y²(这是根号下)z=0及圆柱面x²+y²=R²围城的体积
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![求由锥面z=k/R *√x²+y²(这是根号下)z=0及圆柱面x²+y²=R²围城的体积](/uploads/image/z/13939824-48-4.jpg?t=%E6%B1%82%E7%94%B1%E9%94%A5%E9%9D%A2z%3Dk%2FR+%2A%E2%88%9Ax%26%23178%3B%2By%26%23178%3B%EF%BC%88%E8%BF%99%E6%98%AF%E6%A0%B9%E5%8F%B7%E4%B8%8B%EF%BC%89z%3D0%E5%8F%8A%E5%9C%86%E6%9F%B1%E9%9D%A2x%26%23178%3B%2By%26%23178%3B%3DR%26%23178%3B%E5%9B%B4%E5%9F%8E%E7%9A%84%E4%BD%93%E7%A7%AF)
求由锥面z=k/R *√x²+y²(这是根号下)z=0及圆柱面x²+y²=R²围城的体积
求由锥面z=k/R *√x²+y²(这是根号下)z=0及圆柱面x²+y²=R²围城的体积
求由锥面z=k/R *√x²+y²(这是根号下)z=0及圆柱面x²+y²=R²围城的体积
对于z = F(X,Y),
A =∫∫DDA =∫∫D√[1 +(F X)2 +(F y)的表面积2] DXDY
锥面Z =√(X 2 + Y 2)是圆柱形表面X 2 + Y 2 = 2倍的切削
积分区域D为:0≤X≤2,- √( 2X-X 2)1,0≤Y≤√(2× - ×2)
到极坐标:0≤θ≤2π,0≤R≤2cosθ
削度方程:Z = R;缸公式:R = 2cosθ
的F / X = X / R =COSθ,F Y = Y / R =SINθ
F X)2 +(F Y)2 = COS 2θ+罪2θ= 1
∴A =∫∫D√[1 +(F X)2 +(F Y)2] DXDY
=∫∫e √[1 +1]rdrdθ
=√2∫ [∫ RDR]Dθ
=√2∫ [ R ^ 2/2]Dθ
=√2∫ [2cos 2θ]Dθ
=√2∫ [1 +采用cos2θ] Dθ
=√2/2∫ [1 +采用cos2θ] D(2θ)
=√2/2 [(2θ'+sin2θ)]
=√2/2 [4π-0]
= 2√2π