Question

What is the length of the arc of y=(2/3)x^(2/3) from x=0 to x=3? Explanation needed. :( I know the answer, but I am unsure about the solving technique. Thank you!

Answer 1

Well. There's a formula apparently. Thank for teaching me that collaborative study sites do not work. T_T

Answer 2

What seems to be the problem?

Answer 3

"What is the length of the arc of y=(2/3)x^(2/3) from x=0 to x=3? Explanation needed. :( I know the answer, but I am unsure about the solving technique. Thank you" Obviously, more basic mathematic questions are answered on here, while the more advanced mathematics questions are ignored. These sites are great when you're taking simple math classes, but for the kids in higher math, they are less effective means of obtaining explanations.

Answer 4

I believe the answer is 14/3, which can be obtained with a definite integral formula, for arc lengths.

Answer 5

not it is not 14/3

you can use the formula for arc length
(see http://tutorial.math.lamar.edu/Classes/CalcII/ArcLength.aspx)
use
\[ \frac{dy}{dx} = \frac{4}{9} x^{-\frac{2}{3}} \]
in
\[L= \int\limits_{0}^{3}\sqrt{1+\left(\frac{dy}{dx}\right)^2} dx\]