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. May 6, 2013 #1
    1. The problem statement, all variables and given/known data
    Consider curves ##C_1: (y-x)=(x+y-\sqrt{2})^2## and ##C_2: (x+y-\sqrt{2})=(y-x)^2##, then the area between ##C_1## and ##C_2## is
    A)1/2
    B)1/3
    C)1/4
    D)None


    2. Relevant equations



    3. The attempt at a solution
    Finding out the points of intersection would be a lot difficult here. And even if I find them, integration would be dirty. This is a question from my test paper and I suspect that it has an easy solution but I am unable to figure that out. :confused:

    Any help is appreciated. Thanks!
     
    Last edited: May 6, 2013
  2. jcsd
  3. May 6, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Did you think about trying a change of variables?
     
  4. May 6, 2013 #3
    Nope. How would I do that here? Substitute ##y-x## with ##t##?
     
  5. May 6, 2013 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Sure. Call x+y+sqrt(2)=s, x-y=t. Find the area is s,t coordinates. Don't forget the Jacobian factor.
     
  6. May 6, 2013 #5
    Sorry, never heard of that before. :uhh:

    Hmm...using the substitution, the question is similar to finding area between ##y=x^2## and ##y^2=x##. The area between them is 1/3. This is the answer given in the answer key. Thank you Dick! :smile:
     
  7. May 6, 2013 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

  8. May 6, 2013 #7
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Area between two curves
Loading...