anonymous
  • anonymous
anti-derivative of SQRT(1+(9x- (x^3/3))^2)
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.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
amistre64
  • amistre64
how you wanna do this lol the easy way or the hard way
anonymous
  • anonymous
lets go with easy because this is the part of problems i can never do
amistre64
  • amistre64
\[\sqrt{1+(9x-\frac{x^3}{3})^2}\] lets start by making sure we got the right problem is this it?

Looking for something else?

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

More answers

anonymous
  • anonymous
yes
amistre64
  • amistre64
well; its gonna be a trig sub that turns to int(sec(x)) dx inthe end lol
anonymous
  • anonymous
omg i hate calculus lol
amistre64
  • amistre64
lol...trig sub just cleans it up thats all
anonymous
  • anonymous
yea but i integrated this on my calculator and i still got the wrong answer
amistre64
  • amistre64
\[\int_{} \sqrt{1+tan^2(u)}du\] ;\[u= \frac{27x -x^3}{3}\]
amistre64
  • amistre64
du = 27-3x^2/3 = 9-x^2 dx; maybe that aint a good idea lol
amistre64
  • amistre64
but it shows me another idea lol
anonymous
  • anonymous
yea im not so good with substitution either
amistre64
  • amistre64
u = 9x-x^3 ; du = 9-3x^2 dx {S} sqrt(1+(u/3)^2) du -------------- 9-x^2 maybe?
amistre64
  • amistre64
let me stare blindly at it for a few moments and let my thoughts congeal lol
anonymous
  • anonymous
ok im just trying to follow the process here
amistre64
  • amistre64
we might be better of expanding and combining everything under the radical into one shot
anonymous
  • anonymous
sure i couldnt go anymore wrong with this problem lol
amistre64
  • amistre64
\[\frac{\sqrt{x^6 + 729x^2 -54x^4 +9}}{3}\] is what i get with that ...maybe
anonymous
  • anonymous
yea i got something completely off but u r def prolly right lol
amistre64
  • amistre64
now we can factor under the radical to simply fy things
amistre64
  • amistre64
sooo...how should we factor it :) all polynomials higher then degrees 2 can factor to linears and or irreducibla quads
anonymous
  • anonymous
i honestly have no idea lol
amistre64
  • amistre64
ima try some synthetic stuff and hope i get lucky
anonymous
  • anonymous
lol ok im attempting to do other problems..im going to fail this quiz tomorrow lol
amistre64
  • amistre64
well, the good news is; wolfram couldnt even figure it out lol
anonymous
  • anonymous
whos that? some really smart kid im guessing :)
amistre64
  • amistre64
www.wolframalpa.com type in: int(sqrt(1+(9x-(x^3)/3)^2))dx
anonymous
  • anonymous
o gotcha lol..ok well maybe i went wrong somewhere..the question is find the length of the arch of the parabola y=9-x^2 that lies above the x-axis
amistre64
  • amistre64
wolframalpha.com
amistre64
  • amistre64
.... why you wanna keep secrets from me; i cant read your mind
amistre64
  • amistre64
you had the wrong stuff inputed lol
anonymous
  • anonymous
i did?? well the equation we use is SQRT(1+(dy/dx)^2
amistre64
  • amistre64
\[\int\limits_{} \sqrt{1 + [f'x]^2} dx\]
amistre64
  • amistre64
and is the derivative of 9-x^2 = to the integral of 9-x^2?
anonymous
  • anonymous
yea and the derivative of 9-x^2 is 9x-(x^3/3) right?
amistre64
  • amistre64
dy/dx = -2x
anonymous
  • anonymous
ooo i did the anti derivative didnt i ..i do that all the time because we keep having to switch from derivativeto anti derivative lol
amistre64
  • amistre64
anti derivative is a useless term; later chapters call them what they are inegrals lol
amistre64
  • amistre64
integrals
anonymous
  • anonymous
yea that what we do when we use integrals
amistre64
  • amistre64
{S} sqrt(1+4x^2) dx ; [a,b] whatever your interval s its up there some where
anonymous
  • anonymous
ok now i got it..wow i am retarded lol i do that a lot to
anonymous
  • anonymous
so now how to integrate SQRT(1+4x^2)
amistre64
  • amistre64
easier than you would that other monstrocity lol
anonymous
  • anonymous
i got 2/3(1+4x^2)^(3/2) and then do you also multiply that by the derivative of the inside??
amistre64
  • amistre64
sqrt(1+tan^2(u)) sec^2(u) du ------------------------- 4 sec(u). sec^2(u) du ---------------- 4 sec^3(u) du ---------- 4
amistre64
  • amistre64
got that outta whack a little
anonymous
  • anonymous
ok i g2g i got soccer..but thanks for the help :)
amistre64
  • amistre64
http://www.wolframalpha.com/input/?i=int%28+sqrt%28+1%2B+%28-2x%29^2%29%29+dx+from+-3+to+3

Looking for something else?

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