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!

Area between two curves

  1. Sep 25, 2006 #1
    I am trouble with problems that don't list each function f(x) or g(x). The book sets them equal to y. Every time I do these I'm getting them wrong. When I check the solution, I'm mistaking f(x) for g(x) or vise versa. So is there a way to tell which y is f(x) or g(x)?
  2. jcsd
  3. Sep 25, 2006 #2
    An example might help be helpful.
  4. Sep 25, 2006 #3


    User Avatar
    Homework Helper

    I can't say I understood your question, but refering to the title of the thread, the area between two 'well-behaved' functions f and g on the interval [a, b] is given with [tex]\int_{a}^b(f(x)-g(x))dx[/tex], if f(x) >= g(x), for every x from [a, b].
  5. Sep 26, 2006 #4


    User Avatar
    Staff Emeritus
    Science Advisor

    Of course, the region "ends" where the two curves cross- that is, they have the same y value for that x value. That's why your book "sets them equal to y"- to determine the y values where they cross and thus the limits of integration.
    A little hint- if you area comes out negative, then you have the two curves in the wrong order!
  6. Sep 26, 2006 #5
    This is what I'm talking about:

    Find the area between these two curves-

    Now how do you know which is f(x) or g(x)?
  7. Sep 27, 2006 #6


    User Avatar
    Staff Emeritus
    Science Advisor

    What? Neither is "f(x)" or "g(x)" until you name them! Call whichever you want f and the other g. It might be that your textbook is using a convention that "f" is always the "upper" curve and "g" is always the "lower" curve so that the area is given by [itex]\int (f(x)- g(x))dx[/itex]. If that is the case, then determine which is above the other. Hint: the first is a parabola opening upward, the second a parabola opening downward. You need to decide which is the "upper" curve and which the "lower" curve. You will also need to determine where they intersect.
  8. Sep 27, 2006 #7
    I swear when I worked that problem out it only worked one way. Off the top of my head I had f(x) switched with what the book said. My way was wrong, but then I switched my f(x) for the books way I got the problem right. Had someone double check my math both times and it was good. Thanks for the help!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Area between two curves