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

Question

el_arrow · Answer

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

anonymous · Answer

Start by taking
$$
dV= \pi x^2 dy
$$

anonymous · Answer

$$
y= x^3\
dy = 3 x^2 dx
$$

el_arrow · Answer

okay but why a 2 its x^3

anonymous · Answer

x is the radius of the disk

anonymous · Answer

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

anonymous · Answer

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

el_arrow · Answer

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

anonymous · Answer

if y=1, then x=1
if $ y = x^3=8 $ then x =2

el_arrow · Answer

oh okay i see

el_arrow · Answer

thank you

anonymous · Answer

YW

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

@doulikepiecauseidont

anonymous · Answer

pi*x^2*dy