1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Double Integration, finding Area

  1. Mar 12, 2008 #1
    [SOLVED] Double Integration, finding Area

    1. The problem statement, all variables and given/known data

    Find: [tex]\int[/tex][tex]\int_{A} xdxdy[/tex] , where A is the area between [tex]y=x^2[/tex] and [tex]y=2x+8[/tex]

    2. Relevant equations

    The points of intersection of the two functions is at [tex]x=-2[/tex] and at [tex]x=4[/tex]. Attached is a plot with the area asked to find.

    3. The attempt at a solution

    I'm seeing a problem with the x limits of integration changing at x=-2, one of their intersections. I am pretty sure this can be done by summing the 2 areas separately, but the problem asks to solve for the double integral.
     

    Attached Files:

    Last edited: Mar 12, 2008
  2. jcsd
  3. Mar 12, 2008 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    IF you were to integrate [itex]\int \int x dx dy[/itex], yes, you would have to do it as two separate integrals: as y goes from 0 to 4, x must range between the two sides of the parabola, [itex]x= -\sqrt{y}[/itex] and [itex]x= \sqrt{y}[/itex]. For y between 4 and 16, x ranges from the straight line on the left to the parabola on the right: [itex]x= (1/2)y- 4[/itex] . The integral is given by
    [tex]\int_{y=0}^4\int_{x= -\sqrt{y}}^{\sqrt{y}}x dxdy+ \int_{y= 4}^{16}\int_{x= y/2- 4}^{\sqrt{y}} xdxdy[/tex]

    Are you required to do it in that order? The other order, dydx, would seem to me simpler and more natural. In this case, x must range from -2 to 4 and, for every x, y ranges from [itex]x^2[/itex] to 2x+ 8. In that order, the integral is
    [tex]\int_{x= -2}^4\int_{y= x^2}^{2x+ 8} x dydx[/tex]
     
  4. Mar 12, 2008 #3
    Yeah, that's what I ended up doing. I often get too caught up in small details that prevent me from even starting the problem. This was pretty straightforward once I reversed the order of integration. Once again, thanks for your thorough help. /SOLVED
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Double Integration, finding Area
Loading...