Question

find the length of the curve y=x^2 from x=1 to x=4

Answer 1

Im really confused on how to even start this problem

Answer 2

Arc length of a curve f(x) is given as:
\[\int\limits_{}^{}\sqrt{1+f'(x)^{2}}dx\]

Answer 3

right!

Answer 4

yeah it pretty much the same thing...simplify yours a little more

Answer 5

agree w/ cow.

Answer 6

\[\int\limits_{1}^{4}\sqrt{1+((x^2)')^2} dx=\int\limits_{1}^{4}\sqrt{1+(2x)^2}dx\]

Answer 7

\[\int\limits_{1}^{4}\sqrt{1+4x^2} dx\]

Answer 8

so f(x) = x^2
limits from 1 to 4
what he did ^^

Answer 9

she*

Answer 10

haha my bad...my apologies

Answer 11

you will need a trig substitution here

Answer 12

let tan(theta)=2x

Answer 13

I'm sorry I am really not understanding

Answer 14

all you have to do is use the formula

Answer 15

really?

Answer 16

is it just simply as plugging the 1 and 4 in at this point
\[\int\limits\limits_{1}^{4}\sqrt{1+4x ^{2}}\]

Answer 17

you have to integrate

Answer 18

then plug in limits

Answer 19

remember the fundamental thm of calculus

Answer 20

i thought you are having trouble finding the length
so the trouble is you don't know how to integrate?

Answer 21

ummm ok now i see I will try to find the answer thanks

Answer 22

integration is easy i just forgot how to handle this problem

Answer 23

ok