Results 1 to 3 of 3

Math Help - area between the curves

  1. #1
    Junior Member
    Joined
    Jun 2010
    Posts
    35

    area between the curves

    so I have a question here, in a line of questions, where i am supposed to figure out of a) i need to integrate with respect to x or y, and b)find the area of the region.

    the problem is 4x+y^2=12, x=y. so i figure ill integrate with respect to y, and i move the x over to the other side in the first problem, move the 12 to the left side, then divide everything by 4 to come to 4-(y^2)/4=x now when i sketch this, one of the intercepts is to the left of the y axis, and one is to the right.

    I really don't know where to go at this point.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,453
    Thanks
    1868
    Your first mistake is that you made an arithmetic error in solving 4x+ y^2= 12 for x. 12/4= 3, not 4! x= 3- (1/4)y^2 which is a parabola with x- axis as axis of symmmetry, vertex at (-3, 0), and opening to the right. The line x= y is always the left boundary and the parabola the right boundary of the area they define so you want to subtract the x value of the line from the x value of the parabola to get a positive value: y- (3- (1/4)y^2).

    Yes, one of the points of intersection is to the left of the y-axis and one to the right but that is not really relevant. What are the y coordinates of those points. You want to integrate \int_{y_1}^{y_2} (y- 3+ (1/4)y^2) dy where y_1 is the y coordinate of the lower point and y_2 is the y coordinate of the higher point.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jun 2010
    Posts
    35
    how does it open right? its -(1/4)y^2 isnt it? sorry bout the 4, i was running out the door this morning, and I did have 3 :P also, wouldnt I integrate (3-1/4y^2)-y?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Area Between Curves
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 14th 2011, 02:20 PM
  2. Area between two curves
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 11th 2010, 10:52 PM
  3. area between curves
    Posted in the Calculus Forum
    Replies: 5
    Last Post: January 24th 2010, 04:24 PM
  4. Area between two curves
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 7th 2009, 02:34 AM
  5. Area between two curves
    Posted in the Calculus Forum
    Replies: 6
    Last Post: May 17th 2008, 10:29 PM

Search Tags


/mathhelpforum @mathhelpforum