Results 1 to 4 of 4

Math Help - using integrals to find volume

  1. #1
    Junior Member
    Joined
    Jun 2010
    Posts
    35

    using integrals to find volume

    so i have these 2 problems and for the first one im pretty sure ive done it compleeetely wrong, the second, i dont even know how to start.


    the first one, the directions are find the volume of the solid obtained by rotationg the region bounded by the given curves about the specified line. y= 1/4x^2. y= 5-x^2
    so i used the calculator to give me the intercepts of x=-2, 2 and my integration is going to be pi(5-x^2 - 1/4x^2)^2 i bring the pi out in front of the integral and my next step i want to do is foil out that problem, but that is so massive, it cant be right, so im stuck .

    this second one is the base of s is an elliptical region with boundary curve 9x^2 + 4y^2 = 36. cross sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.

    class was a few days ago, so this isnt the freshest in my brain, especially that second problem, because i cant even remember how to set it up. i appreciate any help i can get
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,884
    Thanks
    673
    Quote Originally Posted by gbux512 View Post
    the first one, the directions are find the volume of the solid obtained by rotationg the region bounded by the given curves about the specified line. y= 1/4x^2. y= 5-x^2
    what is the "specified line" ?

    this second one is the base of s is an elliptical region with boundary curve 9x^2 + 4y^2 = 36. cross sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.
    note that the area of a right isosceles triangle in terms of the hypotenuse, H , is (H^2)/4 , so ...

    hypotenuse length = 2y ... A(x) = y^2 = 9 - (9x^2)/4

    \displaystyle V = 2\int_0^2 A(x) \, dx
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jun 2010
    Posts
    35
    doh, specified line is x axis
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,884
    Thanks
    673
    method of washers ...

    \displaystyle V = \pi \int_a^b [R(x)]^2 - [r(x)]^2 \, dx

    \displaystyle V = \pi \int_{-2}^2 (5-x^2)^2 - \left(\frac{x^2}{4}\right)^2 \, dx
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. using integrals to find volume
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 23rd 2010, 03:43 AM
  2. Integrals - Volume AGAIN
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 15th 2010, 02:17 AM
  3. Integrals - Volume
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 14th 2010, 11:36 PM
  4. Double integrals to find the volume of a solid
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 23rd 2009, 03:38 AM
  5. Volume Integrals?!?!
    Posted in the Calculus Forum
    Replies: 6
    Last Post: December 5th 2008, 11:58 AM

Search Tags


/mathhelpforum @mathhelpforum