Homework Help: Calculating Arc Length

1. Aug 1, 2010

Chandasouk

I need to find the arc length of the function f(x) = 4/5*X5/4 from [0,4].

You have to find f '(x) first and that would be X1/4

I square f '(x) and obtain X1/2 or $$\sqrt{X}$$

I plug it into the formula and get

S = $$\int$$$$\sqrt{1+\sqrt{X}}$$ from [0,4]

I don't know how to evaluate the integral from here though

2. Aug 1, 2010

vela

Staff Emeritus
Don't forget the dx. Try a u-substitution or two.

3. Aug 1, 2010

Imagine a right triangle with the two legs as 1 and $$x^{1/4}.$$ Let $$\theta$$ be the angle opposite $$x^{1/4}.$$
Use this to put $$\sqrt{1 + \sqrt{x} }$$ and $$dx$$ in terms of $$\theta$$ by using some trig operations. Can you get the rest from here?