I am trying to find the volume for the below question using the shell method but I can't get the right answer. can someone give me step by step answer?
$y = x^3, y = 8, x = 0$ about x-axis
what I tried:
$2\pi\int_0^2y(8-y^(3/2))dy$
The answer is $768\pi/7$ but mine isn't even close.
You have some conventions for disk / washers confused with conventions for shells.
First your limits; y goes from 0 to 8. If you were doing disks you would say x from 0 to 2. Next, how high is each shell? $y=x^{1/3}$
$2\pi\int_0^8y(y^{1/3})dy$
via washers:
$\pi\int_0^2 8^2 - x^6 dx$