Question

find the arc length of the function y=((x^4)/8)+1/(4x^2) on the interval [1,2]

Answer 1

what was the formula for arc length.....sqrt(1+dy/dx)?

Answer 2

\[s=\int\limits_{a}^{b} \sqrt{1+(f'(x))^{2}} dx\] I'm pretty sure that's it?

Answer 3

k so forget about that formula for now and focus on finding dy/dx. what do you get?

Answer 4

\[x ^{4}/8 + 1/4x ^{2} \]
I this the right equation or is the whole thing being divided by 4x^2?

Answer 5

\[y'=x ^{3}/2+1/(2x ^{3})\] I got this

Answer 6

yeah that is the first equation

Answer 7

got a -1/2x^3

Answer 8

you forgot a minus sign

Answer 9

oh yeah thanks

Answer 10

k, now that you have that lets combine them and then square it

Answer 11

because the equation is asking for (dy/dx)^2

Answer 12

ok so when you combine them you get this, right?

Answer 13

i got (2x^6 - 2)/(4x^3) when i combined them

Answer 14

\[(x^{6}-1)/4x^{6}\] i got this...

Answer 15

the way you can check to see if its right is to pick any value for x and see if you get the same answer in both the new equation and the old one. lets say x=2. do they equal in your two equations? my equation is actually not simplified. you should get (x^6-1)/2x^3

Answer 16

k im close to the final answer. u still here?

Answer 17

yeah sorry i am still here. after you square it, why isn't it over 4x^6?

Answer 18

i still havent squared it. after you do that it should be (x^6-1)^2/4x^6

Answer 19

oh i see. ok that makes more sense

Answer 20

now looking back at the formula, you know that you have to add 1. so what do you get?

Answer 21

the algebra here is a little tricky. let me know what you get and ill chck it

Answer 22

(x^12+2x^6+1)/(4x^6)

Answer 23

k now factor the top, can you tell me why that will be useful?

Answer 24

oh, because it goes under a square root so you want a perfect square if possible

Answer 25

yup, it works out pretty well so what do you get after taking the square root?

Answer 26

(x^6+1)/(2x^3)

Answer 27

thats what i got. now take the integral from 1 to 2

Answer 28

i got 5/12 as my answer. what did you get?

Answer 29

ummm...not that. I got 123/16

Answer 30

I'll check my math hold on

Answer 31

wolfram says answer is 33/16...so algebra mistake somewhere

Answer 32

yeah, thats what my answer key says also

Answer 33

I found my mistake. Thank you so much! This was really helpful :)

Answer 34

np, but i still havent found my mistake haha. what was your equation after you take the integral?

Answer 35

oh i just found it

Answer 36

(x^4)/8-1/(4x^2)

Answer 37

glad i could help

Answer 38

me to. again, thank you!!