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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?
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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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0it 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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The limits of integrals are from 1 to 4. I tried approximating it but f'(1) is not 0.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i 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)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0if im wrong, let me know :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Will it be right to say? \[f = \int\limits_{a}^{b}x^2/(1+ x^5) dx\] \[f' = x^2/(1+x^5)\]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0that looks proper, except for the a and b part... it gave no interval to find an "area" for right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0isn't the interval [1, 4]?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0nope, 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.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0tell me, can a derivative have more than 1 antiderivative?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lets verify that :) whats the derivative of these 2 equations: y = 3x^2 +6x +10 y = 3x^2 +6x 3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0when you suit it back up it begins to float up and down the y axis right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I see how integrating a derivative can produce a family of functions with a different vertical translations.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0good, 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)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the real issue becomes, what is the integral of that function :) I have not seen an easy way to get it....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Since my teacher rushed through approximation methods today, I guess Ill have to use that. Trapezoidal approximation maybe?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0thats still looking to find the area under the curve, but that is not the question you posted above. do you have the question right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Im pretty sure that was the question. But is the area under x^2/(1+x^5) f?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0No, 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)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0its like you found someones wallet and are trying to find the owner by the limited clues available to you.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we 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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I got an email from my teacher. She said to estimate it and gave three choices: 0.016, 0.376, 0.629.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0then 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 :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Haha... I'm so clueless in calc.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0wish I coulda been more help :) good luck!!
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