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Double Integral:Finding the Area of an Line Intersection.

  1. Mar 26, 2013 #1
    1. The problem statement, all variables and given/known data

    Calculate the area of the figure given by these lines.
    ;x=y
    ;x=2y
    ;x+3y=1
    ;x+3y=2

    2. Relevant equations
    This is the intersection.
    http://www.wolframalpha.com/input/?i=x=y;x=2y+;x+3y=1+;x+3y=2
    http://www4a.wolframalpha.com/Calculate/MSP/MSP27191hcd6420385b0fg300000fg719cb88h13c52?MSPStoreType=image/gif&s=45&w=386.&h=166.&cdf=RangeControl [Broken]
    and i calculate the intesections even tough idk if it's necessary
    • x+3y=1 (2/5 ; 1/5)
    • x=2y

    • x+3y=1 (1/4 ; 1/4)
    • x=y
    • x+3y=2 (4/5 ; 2/5)
    • x=2y

    • x+3y=2 (1/2 ; 1/2)
    • x=y

    3. The attempt at a solution
    Ii's a simple problem i believe but i'm very new to this subject and could'nt get my head around the domain i should integrate.

    ∫∫dxdy = What is the domain to find the area inside the intersection of these lines.
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Mar 26, 2013 #2

    HallsofIvy

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    Science Advisor

    Since your equations are all of the form x= ..., it looks to me like you need to integrate (1- 3y)- 2y from y= 1/5 to y= 1/4, (1- 3y)- y from y= 1/4 to y= 2/5, and (2- 3y)- y from y= 2/5 to y= 1/2.

    Do you see why?
     
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