Results 1 to 6 of 6

Math Help - Integral of an Elipse

  1. #1
    Newbie
    Joined
    Jul 2010
    Posts
    13

    Post Integral of an Elipse

    Hi... again

    I need to calculate the VOLUME of an elipse, but I have no idea how to do it... I assume it would require integration though.

    The cross-sectional function for my elipse is:

    \sqrt{((1-(x-4)^2)/16)*9} ;    0<=x<=6

    and

    -\sqrt{((1-(x-4)^2)/16)*9} ;    0<=x<=6

    which gives:

    Integral of an Elipse-untitled-5.jpg


    So as you can see, I'm trying to calculate the volume from 0 to 6 of this elipse.

    I thought about calculating the volume of the full elipse, then find the proportion of volume i need, but that wouldnt work because it isnt a uniform shape... woudl it?

    Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Failure's Avatar
    Joined
    Jul 2009
    From
    Zürich
    Posts
    555
    Quote Originally Posted by leomylonas View Post
    Hi... again

    I need to calculate the VOLUME of an elipse,
    I suppose you mean the AREA.

    but I have no idea how to do it... I assume it would require integration though.
    Not really, in this particular case. You can get by with just a little geometry+trigonometry, since you can determine the area of that part of the ellipse by multiplying the corresponding area of the circle over its major axis (with diameter 8) by the factor 1/2 (which is the ratio between minor and major axis of the ellipse).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2010
    Posts
    13

    Post

    Quote Originally Posted by Failure View Post
    I suppose you mean the AREA.
    Nope. I mean volume. After a bit more research, I found out what I want to do is called "Volume of Revolution"

    Volume of A Solid of Revolution

    I think I have done this right now.



    However now i have one that is a bit more difficult.

    f(x) = 1/(0.1(x-8)) +0.5; -1.5<=x<=6

    Which means to find the volume i have to calculate this:

    \int_{-1.5}^{6} \pi*(1/0.1(x-8) +0.5)^2 dx

    I've got no idea how to easily integrate that. I could expand it out, but that makes it even harder. Does anyone wanna have a crack at working that one out?

    (Oh, and with the MATH tags, how do you can I make a fraction display properly?)

    Thanks
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466
    You also mean "ellipsoid", not "ellipse".

    To get a fraction, put { and } around what ever you want in the numerator and what ever you want in the denominator. \frac{x^2+ 3xy}{2x- y} gives \frac{x^2+ 3xy}{2x- y}.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by HallsofIvy View Post
    You also mean "ellipsoid", not "ellipse".

    To get a fraction, put { and } around what ever you want in the numerator and what ever you want in the denominator. \frac{x^2+ 3xy}{2x- y} gives \frac{x^2+ 3xy}{2x- y}.
    Ah, to think that I have lived to see the day that HoI would give help on posting with latex (off topic I know but I just had to say it )
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    I don't know... but what if you tried to move a 2d ellipse so that the centre of the ellipse is at the origin?

    Then, you integrate, using the theory of volume of rotation:

    Volume = \pi \int^a_{-a} y^2 dx

    where a and -a are the points where the ellipse cut the x-axis and the curve y is always positive...
    y is then another curve with another formula.

    Or is it not possible this way?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: December 27th 2010, 03:10 AM
  2. Hyperbola and Elipse Equations
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: November 12th 2009, 01:23 PM
  3. "walk" on elipse
    Posted in the Geometry Forum
    Replies: 2
    Last Post: August 5th 2009, 10:25 AM
  4. Basic Conics Help (elipse)
    Posted in the Geometry Forum
    Replies: 2
    Last Post: April 23rd 2006, 03:58 PM
  5. line tangent to an elipse given one point
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 13th 2005, 03:16 AM

Search Tags


/mathhelpforum @mathhelpforum