求绕x轴旋转的旋转体体积，高数定积分

Question

如题所述

Answer 1

y=x^4

y=x^(1/3)

旋转体的体积

=∫[0,1]π[x^(2/3)-x^8]dx

=……

有疑问欢迎追问。

追问

请问答案是22π/45吗？

追答

旋转体的体积
=∫[0,1]π[x^(2/3)-x^8]dx
=π[(3/5)*x^(5/3)-(1/9)*x^9][0,1]
=π[(3/5)-(1/9)]
=π(27/45-5/45)
=π(22/45)
=22π/45