Results 1 to 6 of 6

Math Help - Areas between curves - Which is on top?

  1. #1
    Member
    Joined
    Mar 2009
    Posts
    97

    Areas between curves - Which is on top?

    I seem to be getting in a muddle on finding which function goes on top.

    Can someone help

    I understood it to be the one which has the largest y output when making the points of intersection the argument

    BUT it seems to change on some functions

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Quote Originally Posted by 200001 View Post
    I seem to be getting in a muddle on finding which function goes on top.

    Can someone help

    I understood it to be the one which has the largest y output when making the points of intersection the argument

    BUT it seems to change on some functions

    Thanks

    You have to solve inequalities, of course: after you know the integration interval, you have to solve f(x)>g(x) for the two functions.

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by 200001 View Post
    I seem to be getting in a muddle on finding which function goes on top.

    Can someone help

    I understood it to be the one which has the largest y output when making the points of intersection the argument

    BUT it seems to change on some functions

    Thanks
    If f(x)\geq{g}(x) for all x\in[a,b], then \int_a^b[f(x)-g(x)]dx represents the area between the two curves f and g on [a,b].
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Mar 2009
    Posts
    97
    Thanks
    and if its not then you have to integrate seperately and subtract afterwards?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,977
    Thanks
    1121
    Quote Originally Posted by 200001 View Post
    Thanks
    and if its not then you have to integrate seperately and subtract afterwards?
    No, if f(x)> g(x) on parts of the interval and g(x)> f(x) for other parts, then you will need to integrate (f(x)- g(x)) for the parts where f(x)> g(x), integrate (g(x)- f(x)) for the parts where g(x)> f(x), and add. The point is that "area" is positive and so you must always be integrating a positive function. If f(x)> g(x), then f(x)- g(x)> 0. If g(x)> f(x), then g(x)- f(x)> 0.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Mar 2009
    Posts
    97
    Awesome, that makes sense
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. areas bounded by curves
    Posted in the Calculus Forum
    Replies: 7
    Last Post: May 31st 2011, 12:14 PM
  2. areas between curves
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 14th 2009, 12:57 PM
  3. How to do this Areas between curves question?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 19th 2008, 07:36 PM
  4. Areas under and between polar curves
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 25th 2008, 05:40 PM
  5. Areas Between Curves
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 10th 2007, 02:21 PM

Search Tags


/mathhelpforum @mathhelpforum