Question

Set up the integral for the length of the curve:

Answer 1

\[x=y^{\frac{ 1 }{ 7 }}, 0 \le y \le 2\]

Answer 2

do u know the formul

Answer 3

I know how to do the problem I just want to make sure that I have the correct answer.

Answer 4

using \[\frac{ dx }{ dy } \] as in \[\int\limits \sqrt{1+(x^{'})^2} dy\]

Answer 5

????? I'm lost

Answer 6

well... tehre is no need to solve the integral... just to set up :)

Answer 7

Okay thank you.

Answer 8

\[
\int_0^2\sqrt{1+\left(\frac{dx}{dy}\right)^2}dy
\]

Answer 9

exactly... @aum pretty much derive to find x' and then plug in with the actual value for x

Answer 10

x' = 1/7y^(-6/7)

Answer 11

\[
x = y^{1/7} \\
\frac{dx}{dy} = \frac 17y^{-6/7}
\]

Answer 12

\[
\frac 17\int_0^2\sqrt{49+y^{-12/7}}dy
\]