Results 1 to 2 of 2

Math Help - Double Integral

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    26

    Double Integral

    A sprinkler distributes water in a circular pattern, supplying water to a depth of e^-r at a distance of r feet from the sprinkler.
    A. What is the total amount of water supplied per hour inside a circle of radius 18?
    B. What is the total amount of water that goes through the sprinkler per hour
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,525
    Thanks
    1384
    Quote Originally Posted by Snooks02 View Post
    A sprinkler distributes water in a circular pattern, supplying water to a depth of e^-r at a distance of r feet from the sprinkler.
    Per hour?

    [/quote]A. What is the total amount of water supplied per hour inside a circle of radius 18?
    B. What is the total amount of water that goes through the sprinkler per hour[/QUOTE]

    Imagine a small "piece" of that circle of area dA. The volume of that piece to a depth of e^{-r} is [tex]e^{-r}dA[/itex] you want to integrate that.
    In polar coordinates, dA is  r dr d\theta so for part (A) you need \int_{r=0}^{16}\int_{\theta= 0}^{2\pi} e^{-r} r dr d\theta. For part (B) this is no restriction on r so it is \int_{r=0}^\infty\int_{\theta= 0}^{2\pi} e^{-r} r dr d\theta
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: June 2nd 2010, 02:25 AM
  2. Double Integral and Triple Integral question
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 3rd 2010, 12:47 PM
  3. Double integral (iterated integral)
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 7th 2009, 04:01 PM
  4. Double Integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 12th 2009, 07:48 AM
  5. Replies: 6
    Last Post: May 18th 2008, 06:37 AM

Search Tags


/mathhelpforum @mathhelpforum