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Math Help - integrals increasing.

  1. #1
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    integrals increasing.

    let g be the function given by g(x)=integral (from 1 to x) 100(t^2-3t+2)e^-t^2dt.
    Which of the following statements about g must be true?

    I.g is increasing on (1,2)
    II. g is increasing on (2,3)
    III. g(3)>0
    A) I only
    B) II only
    C) III only
    D) II and III only
    E) I, II, and III
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi

    If g(x)=\int_1^x 100(t^2-3t+2)\exp -t^2 \,\mathrm{d}t, g'(x)=100(x^2-3x+2)\exp -x^2 (fundamental theorem of calculus) and the integral increases if g'(x)>0.
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  3. #3
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    i used fInt and plugged the integral in from one to three for part III. It gave me a neg number so III is not one of the answers

    so, it's B right
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  4. #4
    Super Member flyingsquirrel's Avatar
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    I did not check for g(3)<0 but I agree concerning " g increasing on (2,3)". Don't you have to find a proof of g(3)<0 ?
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