一次問這麼多題實在不恰當 不過時間迫在眉睫，好幾題算到一半卡住，希望板友們能稍微解釋一下我的問題所在: --------------------------------------------------------------------------- Q1.Find the moment of inertia about the Z-axis of a thin shell of constant density δ(δ > 0) cut from the cone 4 x^2 + 4 y^2 - z^2 = 0 , z >= 0 ,by the circular cylinder x^2 + y^2 = 2x 這題要怎麼去計算我大概清楚，但是在找出parametrization(即換成u,v)時找不出適當 的置換方法。 ---------------------------------------------------------------------------- Q2: Find the area of the surfaces: Let S be the portion of the cone z = √(x^2 + y^2) that lies over the region between the circle x^2 + y^2 = 1 and the ellipse 9 (x^2) + 4 (y^2) = 36 in the xy-plane. 跟上題不同的是，我求出了dA = √2 du dv ，但是後面積分的邊界我一時想不出該怎麼 表示出來，因為又有橢圓又有圓，我就卡住了... ------------------------------------------------------------------------------ Q3:Integrate g(x,y,z) = x√(y^2+4) over the surface cut from the parabolic cylinder y^2 + 4z = 16 by the planes x = 0 , x = 1 and z = 0. 跟Q2類似，我把r(u,v)設為( u , v , 4 - (v^2)/4 )然後代入g裡面，以及求出dA，不幸 的是，算出來的答案跟解答不同，正解是56/3。 ------------------------------------------------------------------------------ Q4:A wire of density δ(x,y,z) = 15√(y+2) lies along the curve r(t) = (0,t^2-1,2t),-1 <= t <= 1.Find its center of mass. 這題我目測看出X和Z都是0，但是Y怎麼算都算不出-3/5，所以我想確定一下Ym的算法， 該怎麼下手呢? ------------------------------------------------------------------------------ Q5:Find the center of mass and the moments of inertia about the coordinate axes of a thin wire lying along the curve r(t) = ( t,[2√(2t^3)]/3,(t^2)/2 ), 0 <= t <= 2 , if the density is 1 ( --- ) 1+t 這題感覺跟上一題很像，但是我不知怎麼下手... ---------------- 真的很抱歉一次問五題，在考題轟炸之下已經有點昏頭了，希望板上高手能幫忙我Orz --

※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 122.117.20.246