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

please do this question.
Thank you.

1 Answer
Jul 8, 2017

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.

http://tutorial.math.lamar.edu/

http://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.