高等数学题
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y = 2x^2, x^2 = y/2. x = a 时 y = 2a^2
Vy = π∫<0, 2a^2> (y/2)dy = (π/4)[y^2]<0, 2a^2> = πa^4
Vx = π∫ <a, 2> (2x^2)^2 dx = (4π/5)[x^5]<a, 2> = (4π/5)(32-a^5)
S1 = ∫<0, a>2x^2 dx = (2π/3)[x^3]<0, a> = 2πa^3/3
S2 = ∫<a, 2>2x^2 dx = (2π/3)[x^3]<a, 2> = (2π/3)(8-a^3)
S1 = S2 , a^3 = 8-a^3, a^3 = 4, a = 4^(1/3)
Vy = π∫<0, 2a^2> (y/2)dy = (π/4)[y^2]<0, 2a^2> = πa^4
Vx = π∫ <a, 2> (2x^2)^2 dx = (4π/5)[x^5]<a, 2> = (4π/5)(32-a^5)
S1 = ∫<0, a>2x^2 dx = (2π/3)[x^3]<0, a> = 2πa^3/3
S2 = ∫<a, 2>2x^2 dx = (2π/3)[x^3]<a, 2> = (2π/3)(8-a^3)
S1 = S2 , a^3 = 8-a^3, a^3 = 4, a = 4^(1/3)
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