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Disc Method

  • Thread starter frumdogg
  • Start date
  • #1
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0

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


[tex]\pi[/tex]0[tex]\int[/tex]2(x^3)dx


The Attempt at a Solution



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

Am I on the right path?
 

Answers and Replies

  • #2
Dick
Science Advisor
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618
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?
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
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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


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


The Attempt at a Solution



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

Am I on the right path?
 
  • #4
18
0
Yes, rotating around the x-axis.
 
  • #5
tiny-tim
Science Advisor
Homework Helper
25,832
249
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! :smile:

That doesn't look solid … do you mean y = 2 ? :confused:
 
  • #6
18
0
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.
 
  • #7
tiny-tim
Science Advisor
Homework Helper
25,832
249
hmm … they might as well have said:

y=x^3
x=1;

the rest is just a cylinder. :confused:
 
  • #8
Dick
Science Advisor
Homework Helper
26,258
618
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.
It's a region with y=0 at the bottom and y=x^3 at the top from x equal 0 to 1 and y=1 at the top and y=0 at the bottom from x equal 1 to 2. Halls already set it up for you. tiny-tim is saying the same thing.
 

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