Question

高数问题，定积分求体积

请问体积y是如何得来的，最好能有图解，这类题型一直搞不懂，请教一下方法，谢谢谢谢🙏🙏🙏

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Answer 1

y=x^(1/3) ,x=a, x-轴： y=0
Vx
=π ∫(0->a) y^2 dx
=π ∫(0->a) x^(2/3) dx
= (3/5)π. a^(5/3)
Vy
=π ∫(0->a^(1/3) ) x^2 dy
=π ∫(0->a^(1/3) ) (y^3)^2 dy
=(1/7)π.a^(7/3)
Vy =10Vx
(1/7)π.a^(7/3) = 10[ (3/5)π. a^(5/3)]
(1/7)a^(7/3) = 6a^(5/3)
a^(2/3) =42
a= 42^(3/2)

Answer 2

希望写的比较清楚