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Expert: Alon Mandes - 9/7/2008


Question
please could you help me find the arc length of this curve:x=(y^3/2 -3)-y^1/2...from y=1 to y=9...the hint provided is that 1 +(dx/dy)^2 is a perfect square..any assistance would be appreciated.

Answer
So, our function is x(y)=y^(3/2)-3-y^(1/2). In this case the arc
length is defined by : ∫sqrt[1+x'(y)^2]dy, where y goes from 1 to
9. Of course we can do it differently : ∫sqrt[1+y'(x)^2]dx where x
goes from -3 to 21. You may choose whether to calculate x'(y) or
y'(x). I'll give you both here :

derivative of x with respect to y
x'(y)=1.5y^(0.5)-0.5y(-0.5)
derivative of y with respect to x
1=y'*1.5y^(0.5)-y'*0.5y(-0.5)
y'(x)=1/[1.5y^(0.5)-0.5y(-0.5)]

All you have to do now is calculating the integral.

Alon.

Calculus

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Alon Mandes

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Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

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1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

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Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

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M.A in Mathematics & Bs.c in Electronics.

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