Question

using cylindrical method find the volume generated by rotating the region bounded by \(y = x^3\), \(y = 0\), \(x = 1\) about y = 1

the equation i used is \[\Large 2\pi \int_0^1 (1 - y)(\sqrt[3]{y})dy\] is that right? @dpaInc

Answer 1

pls refresh it

Answer 2

u got it!!!

Answer 3

ninepioverfourteen

Answer 4

so let me get this straight...if the axis of revolution is parallel to y axis...i use dx...if it's parallel to x axis i use dy

the limits i use depend on the "d"

the functions i use depend on the "d"

the radius is the distance of the axis of revolution to the parallel axis minus the variable of integration

there is always a 2 pi outside

Answer 5

umm i can only understand the first and last statements there....
and you're correct assuming we're talking about shells.
the 2pi is outside becuase of the circumference when you rotate the representative rectangle.

Answer 6

im just gonna assume yes to all

Answer 7

i think i know what you're talking about but i don't want to give a definite answer to something i'm unsure of... but....
let's put this way, whatever the width of the representative rectangle is, that's the way i'm integrating.. either dy or dx.

Answer 8

gotta go man.... roha.

Answer 9

roha