1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Calculus: Volume Problems

  1. May 9, 2008 #1
    1.Consider the given curves to do the following.
    x=4+(y-3)[tex]^{2}[/tex], x=8

    Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis. Sketch the region and a typical shell.

    I'm lost on x being a function of y. How do you even enter these into a TI-83? Is there any way to make these easier?

    Here's another one i've been working on that has caused me problems.
    2.The region bounded by the given curves is rotated about the x-axis.
    Find the volume V of the resulting solid by any method.

    First I graphed it:
    htp://img377.imageshack.us/img377/3471/6338ol4.png (Just add another t in http)

    cylindrical shell method
    2 pi r h dr

    I set up an integral. I get confused on determining the radius and height. If i'm rotating around the x-axis, i'm using y's. So, the radius should be y since it's centered around the y-axis. Then what is the shell height? The points at which the parabola crosses the curve are at x=3 and 6. So the shell height should be 6-y, but I think it should be where x = the equation.

    But when I tried to single out x in the equation to get y as a function of x in y=-x[tex]^{2}[/tex]+9x-18, I couldn't calculate it.

    Discs method
    The area of one disc:
    A(x)=[tex]\pi[/tex] * (-x[tex]^{2}[/tex]+9x-18)[tex]^{2}[/tex]

    So the integral is
    [tex]\pi[/tex] times the integral of (-x[tex]^{2}[/tex]+9x-18)[tex]^{2}[/tex] dx

    Now the limits of integration should be from 3 to 6. I then integrated, plugged in the answer to my homework application which prompted me with a predictable "wrong" result. I've had no problems integrating, as i've completed 85% of my homework, but I have a hard time setting these problems up. Especially these odd-ball problems.

    I'm sorry for my vague descriptions. It's hard to describe some of these things over the net. I appreciate any help. Thank you! :smile:
  2. jcsd
  3. May 9, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi RedBarchetta! :smile:
    You can always change any variable letter into any other letter … provided, of course, you remember to change them back at the end!

    Just interchange x and y, to give y = 4+(x-3)², y=8. :smile:
    Forget the word "height" … you need the area of each shell, and the thickness of each shell.

    Then you integrate over the thickness … sometimes it's height, sometimes it's radius, sometimes … :confused:

    In this case, the thickness is not x, but dx.

    Just think of it as "thickness", and you won't be confused! :smile:
    Sorry … I don't understand this … y is a function of x. :confused:

    Show us your working on the integral, and then we can see where the mistake is. :smile:
  4. May 11, 2008 #3
    Thanks for the help Tiny-Tim! I figured both of these out now. :approve:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook