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Why addition? Integral problem

  1. May 22, 2013 #1
    Hello, I can't seem to paste this in. So here is the link.
    http://www.calcchat.com/book/Calculus-ETF-5e/
    It is chapter 7, section 1, question 17.
    Why are you adding ∫ [(x+2) +√4 -x] dx + ∫ 2(√4 -x) dx
    ???
    I'm confused for 2 reasons. Why can you not just evaluate from -5 to 4? ( you will see the bounds I don't know how to put them on my integral here)
    Why must you evaluate from -5 to 0 then from 0 to 4?
    I understand the last term ∫ 2(√4 -x) dx this is 2 times because half is below the x axis.
    But the first part...∫ [(x+2) +√4 -x] dx
    Why would you add them. I can't seem to visualize why this would be. It seems I would find the area under x+2 then subtract that from the area under √4 -x.
    Why not ??
    Thanks,
    J
     
    Last edited: May 22, 2013
  2. jcsd
  3. May 22, 2013 #2

    Mark44

    Staff: Mentor

    They are really subtracting something. What is the equation of the lower half of that parabola?
    Because the formula for the typical area element changes at 0. Between -5 and 0, the typical area element is (yupper - ylower)Δx. After that, yupper is not a value on that line.
     
  4. May 22, 2013 #3
    Yeah Yeah I see. It is a negative.-

    thx
     
  5. May 23, 2013 #4
    Similar question. http://www.calcchat.com/book/Calculus-ETF-5e/
    part b they want you to rotate it about the y axis and in part c about the line x = 3.
    I don't understand this difference in writing for part b....... 3^2 - (y^2)^2

    And in part c they write (3-y)^2 I don't get it.
    It is chapter 7 section 2 question 11.
    Thanks
     
  6. May 23, 2013 #5

    Mark44

    Staff: Mentor

    Seeing that you also started a new thread for this new problem (which is the right thing to do), I am closing this thread.
     
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