Question

Find the arc length of the curve over the given interval. (Round your answer to three decimal places.)
y = ln x, [1, 3]

Answer 1

first find \(f'(x)\)

Answer 2

let me know when you have that

Answer 3

1/x

Answer 4

ok good
now square it

Answer 5

1/x^2

Answer 6

ok, now add 1

Answer 7

okay

Answer 8

this is the easy part, the hard part is coming up

Answer 9

did you get \[\frac{x^2+1}{x^2}\]?

Answer 10

yes

Answer 11

ok and the square root of that is \[\frac{\sqrt{x^2+1}}{x}\]

Answer 12

yes

Answer 13

so now we gotta figure out \[\int_1^3\frac{\sqrt{x^2+1}}{x}dx\]

Answer 14

2.3020

Answer 15

at this point i would just cheat and use a calculator to get the answer,
finding the anti derivative is going to be a pain, require a substitution \[u=\tan(x)\] to get rid of the radical

Answer 16

that is what i get too

Answer 17

Okay! Thank you!

Answer 18

yw