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Regions between curves

  1. Apr 5, 2015 #1
    1. The problem statement, all variables and given/known data
    Find the region bounded by y= 2x and y = x^2 + 3x - 6.
    I found the points of intersection to be x= -3, 2 by setting the equations equal to each other and solving for x.
    I concluded that y = x^2+3x-6 is bigger since I tried a point in between the points of intersection and it came out to be greater.

    2. Relevant equations
    y =2x
    y= x^2+3x-6
    x= -3, 2

    3. The attempt at a solution
    I tried integrating x^2+3x-6 dx from -3 to 2. But it doesn't work. What am I doing wrong?
    I also tried separating the integrals and integrating from -3 to 0, and from 0 to 2, but doesn't seem to work either. The back of my book says that the answer should be 81/32 but I don't know how they got there. Help!
    Thanks!
     
  2. jcsd
  3. Apr 5, 2015 #2
    Forgot to mention it should be integrating x^2+3x-6 - 2x (the other line).
     
  4. Apr 5, 2015 #3

    SammyS

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    Does this mean that now you do know what to integrate ?
     
  5. Apr 5, 2015 #4

    LCKurtz

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    Did you try ##x=0##?
     
  6. Apr 5, 2015 #5
    No, why 0 though? Then y= 2x == 0 and the other equation would be -6. Is that what you mean?
     
  7. Apr 5, 2015 #6
    That's what I tried integrating but its not correct according to my book...
     
  8. Apr 5, 2015 #7

    LCKurtz

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    The reason I suggested trying ##x=0## is it is the easiest, hence less error-prone, number to try. It might have prevented whatever error you made. You have your upper and lower curves reversed.
     
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