# `pi(int_0^1(y^4 - y^8)dy)` Each integral represents the volume of a solid. Describe the solid.

## Expert Answers The formula provided represents the volume of the solid obtained by the rotation of the region bounded by the curves `x = y^2, x = y^4` , the lines x = 0, x = 1, about y axis.

`V = pi*int_0^1 ((y^2)^2 - (y^4)^2)dy`

`V = pi*int_0^1 y^4 dy - pi*int_0^1 y^8 dy`

`V = (pi*y^5/5 - pi*y^9/9)|_0^1`

`V = pi*(1^5/5 - 1^9/9 - 0^5/5 + 0^9/9 )`

`V = pi*(1/5 - 1/9)`

`V = pi*(9-5)/45`

`V = (4pi)/45`

Hence, evaluating the volume of the solid obtained by the rotation of the region bounded by the curves `x = y^2, x = y^4` , the lines `x = 0,` `x = 1` , about y axis, yields `V = (4pi)/45` .

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