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anonymous

  • 5 years ago

If f is the antiderivative of x^2/(1+x^5) such that f(1)=0, then what would f(4) be?

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  1. amistre64
    • 5 years ago
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    anti derive it :)

  2. amistre64
    • 5 years ago
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    it gives you the equation to antiderive and the initial condition of (1,0).... the trick is figuring out a way to get it to antiderive

  3. anonymous
    • 5 years ago
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    The limits of integrals are from 1 to 4. I tried approximating it but f'(1) is not 0.

  4. amistre64
    • 5 years ago
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    i dont think this its asking for the interval of integration when it says f(1) and f(4); its asking you to find the equation that this was gotten from, pinning it down to the point (1,0) and getting the answer for (4,y)

  5. amistre64
    • 5 years ago
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    if im wrong, let me know :)

  6. anonymous
    • 5 years ago
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    Will it be right to say? \[f = \int\limits_{a}^{b}x^2/(1+ x^5) dx\] \[f' = x^2/(1+x^5)\]

  7. amistre64
    • 5 years ago
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    that looks proper, except for the a and b part... it gave no interval to find an "area" for right?

  8. anonymous
    • 5 years ago
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    isn't the interval [1, 4]?

  9. amistre64
    • 5 years ago
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    nope, there is no interval. they want to know a specific value of f at x=4. they give you f(1) = 0 so that you have something to anchor this f(x) with. otherwise it just floats up and down the y axis like a roaming gnome.

  10. amistre64
    • 5 years ago
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    tell me, can a derivative have more than 1 antiderivative?

  11. anonymous
    • 5 years ago
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    Yes, I think.

  12. amistre64
    • 5 years ago
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    lets verify that :) whats the derivative of these 2 equations: y = 3x^2 +6x +10 y = 3x^2 +6x -3

  13. anonymous
    • 5 years ago
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    y'=6x+6

  14. amistre64
    • 5 years ago
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    when you suit it back up it begins to float up and down the y axis right?

  15. anonymous
    • 5 years ago
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    I see how integrating a derivative can produce a family of functions with a different vertical translations.

  16. amistre64
    • 5 years ago
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    good, then when we find a suitable antiderivative, we add a constant to it, a generic "+C" as a place holder; apply the "initial condition" that f(1)=0 and sove for "+C" then we have a valid function with which to determine the value of f(4)

  17. amistre64
    • 5 years ago
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    the real issue becomes, what is the integral of that function :) I have not seen an easy way to get it....

  18. anonymous
    • 5 years ago
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    Since my teacher rushed through approximation methods today, I guess Ill have to use that. Trapezoidal approximation maybe?

  19. amistre64
    • 5 years ago
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    thats still looking to find the area under the curve, but that is not the question you posted above. do you have the question right?

  20. anonymous
    • 5 years ago
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    Im pretty sure that was the question. But is the area under x^2/(1+x^5) f?

  21. amistre64
    • 5 years ago
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    No, the area underneath x^2/(1+x^5) is not f. "f" is the function that will originally be derived down to: x^2/(1+x^5)

  22. amistre64
    • 5 years ago
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    its like you found someones wallet and are trying to find the owner by the limited clues available to you.

  23. amistre64
    • 5 years ago
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    we know that it is some type of cubic rational function; that it has a critical point at x=0.... and if we take another derivative we might be able to see some other clues to it, but figureing out the actual function it came from will be tricky nonetheless

  24. anonymous
    • 5 years ago
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    I got an email from my teacher. She said to estimate it and gave three choices: 0.016, 0.376, 0.629.

  25. amistre64
    • 5 years ago
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    then you try that trap rule and see if that gets you an answer near one of these, if so, then go for it :) but i think I am right about it not being an "area" question.... but Ive been known to be wrong :)

  26. anonymous
    • 5 years ago
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    Haha... I'm so clueless in calc.

  27. anonymous
    • 5 years ago
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    Thanks anyway.

  28. amistre64
    • 5 years ago
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    wish I coulda been more help :) good luck!!

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