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Math Help - Integral Help Please :D

  1. #1
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    Integral Help Please :D

    Hey everyone, hope someone can help me with this problem. I just got back from Spring Break and for some reason have forgotten how to do this... Thanks in advance for any help you can give me!

    Suppose that in a memory experiment the rate of memorizing is given by:
    M'(t)=-0.009t^2+0.2t
    where M'(t) is the memory rate in words per minute. How many words are memorized in the first 10 minutes (from t=0 to t=10) ?
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  2. #2
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    Quote Originally Posted by FGCUguy View Post
    Suppose that in a memory experiment the rate of memorizing is given by:
    M'(t)=-0.009t^2+0.2t
    where M'(t) is the memory rate in words per minute. How many words are memorized in the first 10 minutes (from t=0 to t=10) ?
    integrate words per minute over a period of minutes ...

    number of words = \int_0^{10} M'(t) dt
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    Quote Originally Posted by skeeter View Post
    integrate words per minute over a period of minutes ...

    number of words = \int_0^{10} M'(t) dt
    Thank you for the help, but as dumb as it may sound, I just have no clue where to start. I feel like I don't get taught any of this stuff. Do you have any links or anything that would explain how to integrate the function?
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    Suppose that in a memory experiment the rate of memorizing is given by:
    M'(t)=-0.009t^2+0.2t
    where M'(t) is the memory rate in words per minute. How many words are memorized in the first 10 minutes (from t=0 to t=10) ?


    int(int(-.009t^2 + .2t))

    integrate:

    int(.003t^3 + .1t^2 + c)

    integrate again:

    .00075t^4 + .03333...t^3 +cx +d)

    plug in 10:

    7.5 + 33.333... +10c +d

    245/6 + 10c +d
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    Quote Originally Posted by skeeter View Post
    integrate words per minute over a period of minutes ...

    number of words = \int_0^{10} M'(t) dt
    wait actually i think i sort of remember something, do I find the antiderivative of something and divide it by the other?
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    \int_0^{10} -0.009t^2+0.2t \, dt

    \left[-.003t^3 + 0.1t^2\right]_0^{10}

    [-.003(10^3) + 0.1(10^2)] - [0 + 0]

    -3 + 10 = 7 words
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    wow that helped a ton. Thank you so much. If I'm understanding this correctly, I find the antiderivative and substitute 10 for t, then do the same and substitute 0 for t, and subtract the first (the one i substituted 10) and subtract the second (the one i substituted 0)? If that made any sense haha.
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    Quote Originally Posted by FGCUguy View Post
    wow that helped a ton. Thank you so much. If I'm understanding this correctly, I find the antiderivative and substitute 10 for t, then do the same and substitute 0 for t, and subtract the first (the one i substituted 10) and subtract the second (the one i substituted 0)? If that made any sense haha.
    You find the antiderivative and substract highest from lowest, in this case (t=10) - (t=0) indeed.
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  9. #9
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    Quote Originally Posted by FGCUguy View Post
    wow that helped a ton. Thank you so much. If I'm understanding this correctly, I find the antiderivative and substitute 10 for t, then do the same and substitute 0 for t, and subtract the first (the one i substituted 10) and subtract the second (the one i substituted 0)? If that made any sense haha.
    it's called the Fundamental Theorem of Calculus ... "google" it and learn more.
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