anonymous
  • anonymous
If f is the antiderivative of x^2/(1+x^5) such that f(1)=0, then what would f(4) be?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
amistre64
  • amistre64
anti derive it :)
amistre64
  • amistre64
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
anonymous
  • anonymous
The limits of integrals are from 1 to 4. I tried approximating it but f'(1) is not 0.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

amistre64
  • amistre64
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)
amistre64
  • amistre64
if im wrong, let me know :)
anonymous
  • anonymous
Will it be right to say? \[f = \int\limits_{a}^{b}x^2/(1+ x^5) dx\] \[f' = x^2/(1+x^5)\]
amistre64
  • amistre64
that looks proper, except for the a and b part... it gave no interval to find an "area" for right?
anonymous
  • anonymous
isn't the interval [1, 4]?
amistre64
  • amistre64
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.
amistre64
  • amistre64
tell me, can a derivative have more than 1 antiderivative?
anonymous
  • anonymous
Yes, I think.
amistre64
  • amistre64
lets verify that :) whats the derivative of these 2 equations: y = 3x^2 +6x +10 y = 3x^2 +6x -3
anonymous
  • anonymous
y'=6x+6
amistre64
  • amistre64
when you suit it back up it begins to float up and down the y axis right?
anonymous
  • anonymous
I see how integrating a derivative can produce a family of functions with a different vertical translations.
amistre64
  • amistre64
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)
amistre64
  • amistre64
the real issue becomes, what is the integral of that function :) I have not seen an easy way to get it....
anonymous
  • anonymous
Since my teacher rushed through approximation methods today, I guess Ill have to use that. Trapezoidal approximation maybe?
amistre64
  • amistre64
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?
anonymous
  • anonymous
Im pretty sure that was the question. But is the area under x^2/(1+x^5) f?
amistre64
  • amistre64
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)
amistre64
  • amistre64
its like you found someones wallet and are trying to find the owner by the limited clues available to you.
amistre64
  • amistre64
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
anonymous
  • anonymous
I got an email from my teacher. She said to estimate it and gave three choices: 0.016, 0.376, 0.629.
amistre64
  • amistre64
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 :)
anonymous
  • anonymous
Haha... I'm so clueless in calc.
anonymous
  • anonymous
Thanks anyway.
amistre64
  • amistre64
wish I coulda been more help :) good luck!!

Looking for something else?

Not the answer you are looking for? Search for more explanations.