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因为是绕 y 轴旋转的,那么,每一个微元上:
h = dy,r = x
则:
dV = π * r² * h = π*x²*dy
因为积分曲线是 y = x²,那么,dy = 2x *dx
所以
dV = π*x² * (2x*dx) = 2π*x³*dx
两边同时积分,积分限为 x = 0 → 1。得到:
V = ∫dV
= 2π*∫x³dx
= 2π * (1/4) * x^4|x=0→1
= π/2 * (1 - 0)
= π/2
h = dy,r = x
则:
dV = π * r² * h = π*x²*dy
因为积分曲线是 y = x²,那么,dy = 2x *dx
所以
dV = π*x² * (2x*dx) = 2π*x³*dx
两边同时积分,积分限为 x = 0 → 1。得到:
V = ∫dV
= 2π*∫x³dx
= 2π * (1/4) * x^4|x=0→1
= π/2 * (1 - 0)
= π/2
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