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∫∫∫ dzdydx (z from 0 to 4-2x-2y, y from 0 to 4-2x. x from 0 to 2) = ∫∫ 4-2x-y dydx = ∫ 4y-2xy-y^2/2 [0,4-2x] dx =1/2 ∫ (4-2x)^2 dx =1/2 (16x-8x^2+(4/3) x ^3) [0,2] =16/3

z的積分區間沒有根號耶 直接用球座標轉換 原式=∫∫(9- x ^2-y^2)√( x ^2+y^2) dxdy, x =rcosθ, y=rsinθ =∫∫(9-r^2)r rdrdθ, r:[0...

... 2x-1, 2x+1 :odd 2x , 2x+2 : even 4. the sum of a numver and triple the number x + 3x = 4x 5. ten less than half a number x /2 - 10 6. six reduced...

...0, 0) dV 得 ∫∫_∂R f*g*nx dA = ∫∫∫_R ∂(fg)/∂ x dV 即 ∫∫_∂R f*g*nx dA= ∫∫∫_R f(∂g/∂ x )+g...

...quot; or "second derivative of f" f = "f triple prime" or "third derivative of f" f...可是正式是念 "d over dx" or "take derivative in x " df/dx = 常常是念 "dfdx" 可是正式是念 "...

此題立體區域為柱體,底為xy平面上 x =y^2與y軸圍區域, 上面(z方向) z=0~ 1- x V=∫∫∫_D dz dx dy...1~1]∫[0~y^2]∫[0~1- x ] dz dx dy =∫[-1~1]∫[0~y^2] (1- x ) dx dy =∫[-1~1] ( x -0.5x^2)|[0~y^2] dy =∫[-1~1] (y^2- 0.5y^4) dy = (1/3)y^3- 0.1 y^5 |[-1~1...

29 ( x ^7) = 87 x ^7 = 3 x = 3^(1/7) 29 [3^(1/7)]^y = 150 [3^(1/7)]^y = 150/29 y log [3^(1/7)] = log (150...

...則底面積為向量b,c外積所成之向量的長度值, 又若此外積向量與向量a的夾角為 x ,則柱高為向量a的長度與夾角的正弦值的乘積 所以 V=底面積* 柱高...