# Disc Method

## Homework Statement

Find the volume of a solid formed by revolving the region bounded by graphs of:
y=x^3
y=1
and
x=2

## Homework Equations

$$\pi$$0$$\int$$2(x^3)dx

## The Attempt at a Solution

x^7/7 with boundaries of [0,2]

Am I on the right path?

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Dick
Homework Helper
That's ok if you ignore the y=1 boundary, but I don't think you should. Draw a picture. I presume you are rotating around the x-axis?

HallsofIvy
Homework Helper

## Homework Statement

Find the volume of a solid formed by revolving the region bounded by graphs of:
y=x^3
y=1
and
x=2
Revolved around what axis?

## Homework Equations

$$\pi$$0$$\int$$2(x^3)dx
If you are the x-axis and are using the disk method, you would be integrating $\pi\int_0^1 y^2 dx+ \pi\int_1^2 1 dx$

## The Attempt at a Solution

x^7/7 with boundaries of [0,2]

Am I on the right path?

Yes, rotating around the x-axis.

tiny-tim
Homework Helper
Find the volume of a solid formed by revolving the region bounded by graphs of:
y=x^3
y=1
and
x=2
Hi frumdogg!

That doesn't look solid … do you mean y = 2 ?

The problem says
y=x^3
y=1
x=2

When graphing it, it's a small area with x^3 on the left, y=1 on top, x=2 on right, and x axis on bottom, at least what I am coming up with.

tiny-tim
Homework Helper
hmm … they might as well have said:

y=x^3
x=1;

the rest is just a cylinder.

Dick