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Constant function

  1. Dec 11, 2008 #1
    Suppose that f is integrable on [a,b]. Let c E [tex]\Re[/tex]. Prove that cf is integrable on [a,b] and that
    [tex]\int[/tex] cf= c [tex]\int[/tex] f
    (both integrals goes from a to b i didn't kno how to put it in the integral)

    I'm not sure how to go about this problem
    Please help me out~
    Thanks
     
  2. jcsd
  3. Dec 11, 2008 #2

    HallsofIvy

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    When you are completely "stuck", look back to the definitions.

    How have you defined [itex]\int_a^b f(x) dx[/itex]?
     
  4. Dec 15, 2008 #3
    okay, i just got a hint saying that it would be best if we treat this separately with the cases c[tex]\leq[/tex]0 and c[tex]\geq[/tex]0.

    how would that help me out? wouldn't it just be the same thing except it will be either negative or positive?
     
  5. Dec 15, 2008 #4

    HallsofIvy

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    How have you defined [itex]\int_a^b f(x)dx[/itex]?
     
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