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anonymous
 4 years ago
**Calc 2 Help Needed** Find the length of the arc formed by y = (1/8) * (0.5x^2 16ln(x)) from x=2 to x=6.
anonymous
 4 years ago
**Calc 2 Help Needed** Find the length of the arc formed by y = (1/8) * (0.5x^2 16ln(x)) from x=2 to x=6.

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Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1what seems to be the problem?

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1I assume you know the formula \[\int\limits_{a}^{b}\sqrt{1+(f'(x))^2}dx\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh yes.. I do.. I can't figure out the derivative.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0of y = (1/8) * (0.5x^2 16ln(x))

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1\[\frac{dy}{dx}=\frac{1}{8}\left(x\frac{16}{x}\right)\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ok so now it is sqrt(1+ 1/8 * (x16/x)

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1no...look at the formula again.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I can't bring the 1/8 in? Or shouldn't rather.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ohhh the ^2 wouldn't allow it.

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1\[\frac{1}{8}\left(x\frac{16}{x}\right)\] \[=\frac{1}{8}\left(\frac{x^216}{x}\right)\] \[=\left(\frac{x^216}{8x}\right)\] then 1+square it \[=1+\left(\frac{x^216}{8x}\right)^2\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so how did the top x16 go to x^216?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh common denominator

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1yes...\[x=\frac{x^2}{x}\] for x not equal to zero

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok so after squaring I have 1+ ((x^2  16)^2/64x^2.. Well wolfram did.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok so now I have 64x^2  (x^2  16)^2 all over 64x^2

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1multiply out the numerator...then factor

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so now:( x^4 + 32x^2 + 256) / 64x^2

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1yes...now factor the numerator

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the top would factor to (x^2 + 16)^2

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1yes...now take the square root of the whole thing

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the sqrt would cancel the ^2

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1also it is not 64 anymore

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1close \[\frac{x^2+16}{8x}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ohhh that one.. I am the king of mistakes tonight.

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1write as \[\frac{x^2+16}{8x}=\frac{x^2}{8x}+\frac{16}{8x}=\frac{x}{8}+\frac{2}{x}\] and integrate from 2 to 6

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0OMG why did I do that.. ok let me try again.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I keep getting a negative.

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1what did you get for the integral before evaluating the limits?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Oh wow, I need to integrate..

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Sorry, you probably think I am absolutely dumb.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0After integrating I had x^2/16 + 4/2x

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1\[\int\left(\frac{x}{8}+\frac{2}{x}\right)dx\] \[=\frac{x^2}{16}+2\lnx+c\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok after wolfram it says the second part should contain a log

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.04.19721 with a little confidence.

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1yes...which equals \[2(\ln(3)+1)\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0YESSS!!!!!! I can't believe that simple problem turned so nasty!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Would you care to help me solve another?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I'll start a new problem of course.

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1hmmm...don't know if I have that much time. post it in a new thread...someone will help...If I have time I'll look

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Okay thanks so much.. Were you by any chance a math major?

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1so yes...I was a math major

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1I don't give out that info :)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ahhh.. haha, I understand. Well I'm a student at a SEC school. Hopefully you aren't my teacher.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Haha okay.. Well thanks again for the help. This stuff is hard to understand in a lecture hall.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Thank you. Have a great night.
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