Results 1 to 2 of 2

Math Help - Double and triple integral issues

  1. #1
    Newbie
    Joined
    Jun 2008
    Posts
    22

    Double and triple integral issues

    I'm having a really hard time trying to figure out how to find the limits of double and triple integrals.

    I'm also having trouble determining which limits go on which integral and whether it should be ordered dydx or dxdy, etc.

    Here's a few problems from the book:

    Find the area of the region R that lies below the parabola y=4x-x^2 above the x-axis, and above the line y=-3x+6.

    It shows that area = \int_{1}^{2} \int_{-3x+6}^{4x-x^2} dydx + \int_{2}^{4} \int_{0}^{4x-x^2} dydx (I'm not sure what's wrong with the LaTeX? here's what I used: \int_{1}^{2} \int_{-3x+6}^{4x-x^2} dydx + \int_{2}^{4} \int_{0}^{4x-x^2} dydx )

    No idea how they got those limits.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by dataspot View Post
    I'm having a really hard time trying to figure out how to find the limits of double and triple integrals.

    I'm also having trouble determining which limits go on which integral and whether it should be ordered dydx or dxdy, etc.

    Here's a few problems from the book:

    Find the area of the region R that lies below the parabola y=4x-x^2 above the x-axis, and above the line y=-3x+6.

    It shows that area = \int_{1}^{2} \int_{-3x+6}^{4x-x^2} dydx + \int_{2}^{4} \int_{0}^{4x-x^2} dydx (I'm not sure what's wrong with the LaTeX? here's what I used: \int_{1}^{2} \int_{-3x+6}^{4x-x^2} dydx + \int_{2}^{4} \int_{0}^{4x-x^2} dydx )

    No idea how they got those limits.
    Have you drawn a careful sketch of the region? Note that one of the intersection points of the line and the parabola is (1, 3):

    -3x + 6 = 4x - x^2 => x^2 - 7x + 6 = 0 => (x - 6)(x - 1) = 0 => x = 1, 6.

    If you integrate first with respect to y, then there are two distinct subregions:

    R1: From y = -3x + 6 to y = 4x - x^2. And note that x goes from 1 to 2. Set up the integral ......

    R2: From y = 0 (the x-axis) to y = 4x - x^2. And note that x goes from 2 to 4. Set up the integral ......
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: November 14th 2010, 06:01 PM
  2. Replies: 3
    Last Post: July 26th 2010, 01:46 AM
  3. Double Integral and Triple Integral question
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 3rd 2010, 12:47 PM
  4. Double Angle ID issues, did my teacher grade wrong?
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: April 26th 2009, 10:11 AM
  5. double and triple integration
    Posted in the Calculus Forum
    Replies: 6
    Last Post: April 26th 2007, 09:48 AM

Search Tags


/mathhelpforum @mathhelpforum