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Math Help - Fundamental Theorem of Calculus

  1. #1
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    Fundamental Theorem of Calculus

    Working on some homework problems, and kind of stuck. I thought I had a handle on this, but not so much.

    Here is the problem:



    What I did is take the anti derivative, which is t^5/5.. then plug in the values and subtract. So I get 20^5/5 - x^5/5 to be the answer.. but thats wrong. I don't know if I'm missing a step or doing something wrong. Any help would be greatly appreciated.

    Thanks!
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Chetti View Post
    Working on some homework problems, and kind of stuck. I thought I had a handle on this, but not so much.

    Here is the problem:



    What I did is take the anti derivative, which is t^5/5.. then plug in the values and subtract. So I get 20^5/5 - x^5/5 to be the answer.. but thats wrong. I don't know if I'm missing a step or doing something wrong. Any help would be greatly appreciated.

    Thanks!
    I'm sorry, but I don't see the integral... xD
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  3. #3
    Senior Member Sampras's Avatar
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    Is it  \int_{x}^{20} t^4 \ dt ?
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  4. #4
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    yes, its t^4 (thats the integral) and the limits are 20 (a) and x (b)
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  5. #5
    Senior Member Sampras's Avatar
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    Quote Originally Posted by Chetti View Post
    yes, its t^4 (thats the integral) and the limits are 20 (a) and x (b)
    Then it would be  \frac{x^5}{5}- \frac{20^{5}}{5} .
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  6. #6
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    Thanks! I can't log into where I have to go to try that, but its a little different from what I was trying to do.

    Thanks again!!
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  7. #7
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    The answer was wrong. I eventually did get the right answer, and I will post back with it, I need to log in to the site and get it. BUT, I was missing a step.

    Here are the steps: antiderivative, then plug in the limits then take the derivative, then subtract.. then you get the answer. I was so confused. I'm still confused.
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  8. #8
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    \int_x^{20} t^4 \, dt = \frac{20^5}{5} - \frac{x^5}{5}


    but why do I get the feeling that this is not all there is to it?

    note that the original "problem" was given as a function ... f(x) = \int_x^{20} t^4 \, dt

    sure you weren't supposed to find f'(x) ?
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  9. #9
    Senior Member Twig's Avatar
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    If you are looking for f'(x) ...

    f(x)=\int_{x}^{20}t^{4}\; dt = - \int_{20}^{x}t^4\; dt \; ,\Rightarrow f'(x)= -x^{4}
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