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Identities theorem problem

  1. Jun 21, 2005 #1
    I need help on the following problem. (attached)

    Thanks
     

    Attached Files:

  2. jcsd
  3. Jun 21, 2005 #2
    Draw a picture of some curve (i.e. make a guess about what the curve looks like), shade the regions given, then think about what they are asking -- perhaps the answer will become obvious...
     
  4. Jun 21, 2005 #3
    hello there

    well
    f '(5)-f '(2) =11
    f '(11)-f '(8) =27
    f '(5)-f '(8)+f '(11)-f '(2)=f '(5)-f '(2)+f '(11)-f '(8) =11+27=38
    I hope you do know what i have done, take care

    steven
     
  5. Jun 21, 2005 #4
    I'm not sure if 38 is the correct answer though
     
  6. Jun 21, 2005 #5
    can you explain how you got to that part? :cool:
     
  7. Jun 21, 2005 #6
    hello there

    why arnt you sure, what are you having doubts about? explain your thoughts?

    steven
     
  8. Jun 21, 2005 #7
    even though i scanned it in there, it was a mere guess.
     
  9. Jun 21, 2005 #8
    hello there

    well I have basically given you the answer all you have to do now is interpret it, you must have some prior knowledge of knowing the basics of how to understand this question, by the way they were suppose to be capital F's

    F(5)-F(2) =11
    F(11)-F(8) =27
    F(5)-F(8)+F(11)-F(2)=F(5)-F(2)+F(11)-F(8) =11+27=38

    steven
     
  10. Jun 21, 2005 #9
    can you state the theorem or definition that makes that true? I understand the format it's in, but not why it works. Even visualizing it doesnt make sense :(
     
  11. Jun 21, 2005 #10
    actually, i drew myself a picture, and now i understand it now :)
     
  12. Jun 21, 2005 #11
    guess a picture is worth a thousand words... here it is attached
     

    Attached Files:

  13. Jun 21, 2005 #12
    i really appreciate the quick response... that's what makes physicsforums a great place!!!!
     
  14. Jun 21, 2005 #13
    you welcome

    well we are happy for you to be part of this forum, by the way you havnt told us what your answer was?
     
  15. Jun 25, 2005 #14
    When i was doing that problem, I had originally put the answer as 38 because somewhere in the back of my mind i had recalled reading about adding and subtracting integrals.

    I didnt understand what the answer was, but after i drew the picture, it became more clear :) The answer is 38.
     
  16. Jun 25, 2005 #15
    [tex]\int_a^b f(x) dx =\int_a^c f(x) dx +\int_c^b f(x) dx[/tex]
    [tex]\int_a^b f(x) dx =-\int_b^a f(x) dx[/tex]
    Do you know these identities?
    These 2 make given problem almost formal.
     
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