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Calc 2 final tomorrow need help

  1. Dec 10, 2009 #1
    calc 2 final tomorrow need urgent help!!

    Evaluate the derivative of the function

    G(x) = ({integral} from x to x^2) of sin(-t^2)dt

    this was on my review for the final and i just cannot get an answer. any help will be greatly appreciated.
     
  2. jcsd
  3. Dec 10, 2009 #2
    need help evaluating derivative of sin(x^2)

    sorry i'm new to this site.
    i tried substitution which did not get me anywhere.

    next, i did taylor series but could not get an answer.

    now i am stuck. i am almost positive i have to use a taylor series.

    with the series i got

    x^2 - (x^6)/3! + (x^10)/5! ...

    i plugged in x^2 for x
    and i plugged in x for x and subtracted the two and got another series...
    now what? antidifferentiate the series and say that that is my answer or did i mess up somewhere?
     
  4. Dec 10, 2009 #3

    tiny-tim

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    Welcome to PF!

    Hi calchelp! Welcome to PF! :smile:

    (have an integral: ∫ and try using the X2 tag just above the Reply box :wink:)
    Hint: fundamental theorem of calculus. :wink:
     
  5. Dec 10, 2009 #4
    Re: calc 2 final tomorrow need urgent help!!

    can i change the title of this thread??
     
  6. Dec 10, 2009 #5
    Re: calc 2 final tomorrow need urgent help!!

    is the answer:

    sin(-x^4)2x - sin(-x^3)
     
  7. Dec 10, 2009 #6

    tiny-tim

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    Almost … where did your x3 come from? :confused:
     
  8. Dec 10, 2009 #7
    Re: calc 2 final tomorrow need urgent help!!

    ok... so after about 20 minutes of looking at it i realized that i completely made up the x^3 i dont know why or where it came from...

    so is the answer:
    sin(-x^4)2x - sin(-x^2)

    please tell me that is right. i am about to go insane!!!
     
  9. Dec 10, 2009 #8
    Re: calc 2 final tomorrow need urgent help!!

    can anyone confirm this please?
     
  10. Dec 10, 2009 #9

    Dick

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    Re: calc 2 final tomorrow need urgent help!!

    That's right.
     
  11. Dec 10, 2009 #10
    Re: calc 2 final tomorrow need urgent help!!

    thank you! dick and tiny-tim!!
     
  12. Dec 10, 2009 #11
    Re: calc 2 final tomorrow need urgent help!!

    Essentially this is using the chain rule whereby when:

    G(x) = (integral of f1(x) to f2(x) ) g(t) dt

    G'(x) = g(f2(x))*f2'(x) - g(f1(x))*f1'(x)

    so in your case, G'(x) = sin(-x^4)*2x - sin(-x^2)
     
  13. Dec 11, 2009 #12

    tiny-tim

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    Hi calchelp! :smile:

    (just got up :zzz: …)
    You can tidy it up a bit by taking the minus out of the sin (because sin(-θ) = -sinθ) …

    sin(x2) - 2x*sin(x4) :wink:
     
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