Question

Find the length of the curve y=x^(2/3) x=0, x=3

Answer 1

\[\int\limits_{0}^{3}\sqrt{1+(4/9)x^{-2/3}}dx\]

Answer 2

write in terms of y instead
your adventure should be much easier

Answer 3

\[x=y^\frac{3}{2} , y=0 \text{ \to } y=3^\frac{2}{3} \\ x'=\frac{3}{2}y^\frac{1}{2} \\ (x')^2=\frac{9}{4}y \\ \int\limits_0^{3^{\frac{2}{3}}} \sqrt{1+\frac{9}{4} y} dy\]
use a substitution for the inside v=1+9y/4

Answer 4

thanks you were right, it made things so much easier

Answer 5

http://tutorial.math.lamar.edu/Classes/CalcII/ArcLength.aspx
Pauls notes does a similar one if you wanted more examples.
And I'm glad it helped you. :)