Question

use the disk method to find the volume of the solid formed by revolving the region bounded by the graph of y=x^3, the y-axis and the lines y=1 and y=8 about the y-axis

Answer 1

i dont know how to do this problem can you help please

Answer 2

Start by taking
\[
dV= \pi x^2 dy
\]

Answer 3

\[
y= x^3\\
dy = 3 x^2 dx
\]

Answer 4

okay but why a 2 its x^3

Answer 5

x is the radius of the disk

Answer 6

\[
dV= \pi x^2 ( 3 x^2 dx)= 3 \pi x^4 dx
\]

Answer 7

\[
V= \int_1^2 3 \pi x^4 dx
\]
Compute the integral and you are done

Answer 8

where do you get the 2 and 1? you dont use the y=1 and y=8?

Answer 9

if y=1, then x=1
if \( y = x^3=8 \) then x =2

Answer 10

oh okay i see

Answer 11

thank you

Answer 12

YW

Answer 13

@eliassaab where did you get that theory from? About the dV=pi*x^2*dy?

Answer 14

What is the volume of a disk of radius x and thickness dy?

Answer 15

@doulikepiecauseidont

Answer 16

pi*x^2*dy