Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integrating Areas between curves

  1. Apr 26, 2012 #1
    I can't figure how to solve this problem. Is says ∫∫(x^2)y dA where R is the region bounded by curves y=(x^2)+x and y=(x^2)-x and y=2. I can't figure how to do the limits with that. Please help!
     
  2. jcsd
  3. Apr 26, 2012 #2

    [itex]y=x^2+x[/itex] is an ascending straight parabola with zeroes at [itex]-1\,,\,0[/itex] , and [itex]y=x^2-x[/itex] is a similar such parabola with zeroes at [itex]0\,,\,1[/itex].

    Well, now draw both parabolas together, find their intersection points and...voila!

    DonAntonio
     
  4. Apr 26, 2012 #3
    I was able to get all that. I even graphed it but I can't figure out how to go about writing the integral.
     
  5. Apr 26, 2012 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Where do the two parabolas intersect? Where does y= 2 intersect the two parabolas?

    It looks to me that you will want to do this in two separate integrals. First, take x from the value of x where the line y= 2 intersects [itex]y= x^2+ x[/itex] to x= 0. You should be able to see that, for each x, y goes from the parabola up to [itex]y= x^2+ x[/itex]. Then do the second integral from x= 0 to the intersection of y= 2 and [itex]y= x^2- x[/itex].
     
  6. Apr 28, 2012 #5
    Hey man,you should do this in 2 double integrals-
    0 2
    ∫ ∫ f(x,y) dy dx
    -1 (x(x-1))

    1 2
    ∫∫ f(x,y) dy dx
    0 (x(x+1))


    and then add the 2 for your total volume.
    I hope this is right :smile:
     
    Last edited: Apr 28, 2012
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Integrating Areas between curves
  1. Area between two curves (Replies: 14)

  2. Areas between curves (Replies: 1)

  3. Area between curves (Replies: 7)

Loading...