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Math Help - The Fundamental Theorem of Calculus

  1. #1
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    The Fundamental Theorem of Calculus

    Let g(x)= \int_0^x f(t)dt, where f is the function whose graph is shown.


    g(0) = 0
    g(3) = 4.5
    g(6) =
    g(9) =
    g(12) =
    g(15) =
    g(18) =


    I got the first two, but I guess I am just not getting the rest, if you could help me with how to set the up the others.

    I thought g(6) you would take the 4.5 and subtract the area of the triangle that goes below the x-axis to give you -9, but the computer is telling me thats wrong. Please help!
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  2. #2
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    Quote Originally Posted by ryan18 View Post
    Let g(x)= \int_0^x f(t)dt, where f is the function whose graph is shown.


    g(0) = 0
    g(3) = 4.5
    g(6) = 0
    g(9) = -4.5
    g(12) = 0
    g(15) = 13.5
    g(18) = 36
    just a process of summing signed areas between the curve and the x-axis.

    integrating from left to right ... area above the x-axis is positive, area below is negative.
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  3. #3
    Super Member Deadstar's Avatar
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    Quote Originally Posted by ryan18 View Post
    Let g(x)= \int_0^x f(t)dt, where f is the function whose graph is shown.


    g(0) = 0
    g(3) = 4.5
    g(6) =
    g(9) =
    g(12) =
    g(15) =
    g(18) =


    I got the first two, but I guess I am just not getting the rest, if you could help me with how to set the up the others.

    I thought g(6) you would take the 4.5 and subtract the area of the triangle that goes below the x-axis to give you -9, but the computer is telling me thats wrong. Please help!
    g(6) = 0 since area above y-axis = area below y-axis.

    (and also, 4.5 - 9 = -4.5... hint for g(9))
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