Question

Describe the solid whose volume is represented by `int_(0)^(3) (2pi x^5)dx`. ?

please do this question.
Thank you.

Answer 1

Recall that a solid of revolution about the `y` axis is given in general for the shell method by

`V = 2pi int_(a)^(b) xr(x)dx`,

where `r(x)` describes the shape that will be revolved around a vertical axis, `x` indicates the distance of the function's edge to the rotational origin, and `2pi` is the circumference in radians.

![tutorial.math.lamar.edu)

![tutorial.math.lamar.edu)

In this case, you have `r(x) = x^4` from `x = 0 -> 3`.

Wolfram Alpha

I assume it is rotated about `x = 0`. If so, it is going to look like a cylinder with an upside-down-silo-shaped hole.