Solving for Arc Length
Date: 9/10/96 at 16:9:0 From: Chris Garver Subject: Length of Curve Greetings, Would you please show me how to solve for the arc length of f(x) = 1/3 (x^2 + 2)^(3/2), from [0,2]? The answer is supposed to be 14/3, but I'm having difficulty getting that result. I would very much like to see a solution for this problem. Thank you, Chris
Date: 9/24/96 at 22:5:27 From: Doctor Jerry Subject: Re: Length of Curve Dear Chris, The arc length formula is the integral from a to b of sqrt(1+y'^2)dx. I will not go into a proof of why this holds true (if you have questions, feel free to write). y'=(1/2)[(x^2+2)^(1/2)]*2x=x*(x^2+2)^(1/2). It then follows that sqrt(1+y'^2) = sqrt(1+(x^2)*(x^2+2))=sqrt(x^4+2x^2+1). I feel confident that you can recognize the stuff inside the square root as a perfect square. After that, the problem is easy. I get 14/3. -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Date: 9/25/96 at 7:48:13 From: Chris Garver Subject: Re: Length of Curve Thanks for the help. - Chris
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