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G(x) is the antiderivative of F(x) with G(1) = 1; Find a formula for G(x)

  1. Apr 13, 2012 #1
    G(x) is the antiderivative of F(x) with G(1) = 1; Find a formula for G(x)....

    Find a formula for G(x) in terms of F(x).

    I would have just written [tex]\int_0^x{F(x)dx}[/tex] but I know the value G(1) = 1 has to be included somewhere. Can someone help me figure this one out?
     
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  3. Apr 13, 2012 #2

    Dick

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    Re: G(x) is the antiderivative of F(x) with G(1) = 1; Find a formula for G(x)....

    How about if you just add a constant?
     
  4. Apr 13, 2012 #3
    Re: G(x) is the antiderivative of F(x) with G(1) = 1; Find a formula for G(x)....

    [tex]\int_0^x{F(x)dx} + C[/tex]??
     
  5. Apr 13, 2012 #4

    Dick

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    Re: G(x) is the antiderivative of F(x) with G(1) = 1; Find a formula for G(x)....

    Sure. If that is your G(x) then what value of C will make G(1)=1? Put x=1 and solve for C.
     
  6. Apr 13, 2012 #5
    Re: G(x) is the antiderivative of F(x) with G(1) = 1; Find a formula for G(x)....

    Well, wouldn't I need to know what the value of [tex]\int_0^1{F(x)dx}[/tex] is to determine that?
     
  7. Apr 13, 2012 #6

    Dick

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    Re: G(x) is the antiderivative of F(x) with G(1) = 1; Find a formula for G(x)....

    No. You can't compute it. [tex]\int_0^1{F(x)dx}[/tex] should appear as part of your answer.
     
  8. Apr 13, 2012 #7
    Re: G(x) is the antiderivative of F(x) with G(1) = 1; Find a formula for G(x)....

    [tex]G(x) = 1 + \int_1^xF(s)ds[/tex] ?
     
  9. Apr 13, 2012 #8

    Dick

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    Re: G(x) is the antiderivative of F(x) with G(1) = 1; Find a formula for G(x)....

    Good job. Why the '?'
     
  10. Apr 13, 2012 #9
    Re: G(x) is the antiderivative of F(x) with G(1) = 1; Find a formula for G(x)....

    I wasn't sure of the limits of integration. They were kind of unjustified.
     
  11. Apr 13, 2012 #10

    Dick

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    Re: G(x) is the antiderivative of F(x) with G(1) = 1; Find a formula for G(x)....

    If you'd followed the line I was suggesting you should have found [tex]C=1-\int_0^1{F(s)ds}[/tex]

    Can you justify the bounds using that?
     
  12. Apr 13, 2012 #11
    Re: G(x) is the antiderivative of F(x) with G(1) = 1; Find a formula for G(x)....

    The F(x) was making it confusing.
     
  13. Apr 13, 2012 #12

    Dick

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    Re: G(x) is the antiderivative of F(x) with G(1) = 1; Find a formula for G(x)....

    Maybe. If one of the limits of integration is x you shouldn't write the integral dx. Since the integration variable is a dummy you should use something besides x, like s. Makes life less confusing.
     
  14. Apr 13, 2012 #13
    Re: G(x) is the antiderivative of F(x) with G(1) = 1; Find a formula for G(x)....

    Can you explain why C would allow you to justify the bounds.
     
  15. Apr 13, 2012 #14

    Dick

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    Re: G(x) is the antiderivative of F(x) with G(1) = 1; Find a formula for G(x)....

    The integral from 0 to x of F minus the integral from 0 to 1 of F equals the integral from 1 to x of F.
     
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