Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fundament Confusion

  1. Sep 25, 2004 #1
    Hello page...im taking integral calculus and we are past integration of improper integrals. I know how to use the fundamental theorm but i dont get the first part...[itex] \frac{d}{dx}\int^x_af(t)dt=f(x)[/itex]

    the book used it in an example....find the dirivative of [tex]g(x)=\int_0^1\sqrt{1+t^2}dt[/tex]....the book goes on to tell you the answer but it show NO STEPS...it is James Stewart Calculus 2nd edition i believe if anyone has the same book..page 383..but anyway can some one go through the steps...plz :redface:
     
    Last edited: Sep 25, 2004
  2. jcsd
  3. Sep 25, 2004 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    There is something wrong in the statement of the problem. You have g(x) = something, where x does not appear. As stated g'(x)=0.
     
  4. Sep 25, 2004 #3
    sorry I copied down the problem wrong...this is the correct one


    [tex]g(x)=\int_0^x\sqrt{1+t^2}dt[/tex]
     
  5. Sep 25, 2004 #4

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    just plug into the statement you gave of the ftc. this is a special case. i.e. what is f(t) here?
     
  6. Sep 25, 2004 #5

    Tide

    User Avatar
    Science Advisor
    Homework Helper

    We can get it from first principles:
    [tex]\frac {dg}{dx} = \lim_{h \rightarrow 0} \frac {\int_0^{x+h} \sqrt{1+t^2} dt - \int_0^{x} \sqrt {1+t^2} dt}{h}[/tex]
    [tex]\frac {dg}{dx} = \lim_{h \rightarrow 0} \frac {\int_{x}^{x+h} \sqrt{1+t^2} dt}{h}[/tex]
    [tex]\frac {dg}{dx} = \lim_{h \rightarrow 0} \sqrt{1+x^2} \frac {\int_{x}^{x+h} dx}{h} = \sqrt {1+x^2}[/tex]
     
  7. Sep 25, 2004 #6

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    what "first principle" did you use in the next to last step?
     
  8. Sep 26, 2004 #7

    JasonRox

    User Avatar
    Homework Helper
    Gold Member

    I got the fifth edition, so I can't help you there. I just hope I don't encounted similiar problems.
     
  9. Sep 26, 2004 #8

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    what problems do you think the OP encountered in the book? the solution is self evident and any problems the OP had are nothing to do with the book. the book has many faults, if it's the one i think it is, but that isn't one of them.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Fundament Confusion
Loading...