Question

高数，定积分几何问题？

第七大题，求绕y轴的体积。答案看不懂

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Answer 1

y=e^x
x轴: y=0
y轴: x=0
x=1
Vx
=π∫ y^2 dx
=π∫(0->1) e^(2x) dx
=(π/2 )[ e^(2x) ]|(0->1)
=(π/2 )( e^2 -1 )
//
x=1
y=e^x = e
Vy
=π∫ x^2 dy
=π∫ (0->e) (lny)^2 dy
=π[y(lny)^2]| (0->e) -2π∫ (0->e) lny dy
=πe - 2π[ylny]|(0->e) +2π∫ (0->e) dy
=πe - 2πe +2πe
=πe

Answer 2

35926了超