Results 1 to 2 of 2

Math Help - Llimits for a nested integral

  1. #1
    Member
    Joined
    Oct 2007
    Posts
    159

    Llimits for a nested integral

    I need to set up the double integral (but not solve) that applies to:

    For the volume of the solid below the graph of f(x,y) = 25 - x^2 - y^2 and above the plane z = 16

    Would the limits of the outside integral be -5 to 5 and for the inner integral from (16 - y^2)^1/2 to (25 - y^2)^1/2 of 25 - x^2 - y^2 dy dx?????
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by Frostking View Post
    I need to set up the double integral (but not solve) that applies to:

    For the volume of the solid below the graph of f(x,y) = 25 - x^2 - y^2 and above the plane z = 16

    Would the limits of the outside integral be -5 to 5 and for the inner integral from (16 - y^2)^1/2 to (25 - y^2)^1/2 of 25 - x^2 - y^2 dy dx?????
    It would be easier if you did this in polar coordinates.

    We can find the r bounds by looking at the cross section of z=25-x^2-y^2=25-r^2 and z=16.

    Thus, 16=25-r^2\implies r^2=9. This is a circle of radius r=3.

    Thus, we see that we need to have 0\leqslant r\leqslant 3 and 0\leqslant\theta\leqslant2\pi to generate the circle.

    Thus, our integral would be \int_0^{2\pi}\int_0^3 \left(25-r^2\right)r\,dr\,d\theta=\int_0^{2\pi}\int_0^3 25r-r^3\,dr\,d\theta

    Does this make sense?

    EDIT: Fixed a typo on my part...sorry =]
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Nested set question
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: August 31st 2009, 03:09 AM
  2. Nested sets
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: August 27th 2009, 10:11 PM
  3. Nested integral in spherical coordinates
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 8th 2009, 11:26 PM
  4. Nested integral problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 3rd 2009, 09:46 AM
  5. Nested Quantifiers
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 23rd 2009, 03:41 PM

Search Tags


/mathhelpforum @mathhelpforum