(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the length of the curve r(t) = <2t^{3/2}, cos 2t, sin 2t>, for 0<= t <=1

2. Relevant equations

L = [tex]\int\sqrt{(dx/dt)^2+(dy/dt)^2+(dz/dt)^2}dt[/tex]

3. The attempt at a solution

(dx/dt)^{2}= (3t^{1/2})^{2}

(dy/dt)^{2}= (-2 sin(2t))^{2}

(dz/dt)^{2}= (2 cos(2t))^{2}

[tex]\int\sqrt{9t+4sin^2 (2t) + 4 cos^2 (2t)}dt[/tex]

and since sin^2 + cos^2 = 1, that reduces to:

[tex]\int\sqrt{9t+4}dt[/tex]

I found a site that had an identity for integrals with square roots, and this resembles number 6 on the list:

http://www.sosmath.com/tables/integral/integ4/integ4.html

so using that identity, I get

[tex]2\sqrt{(9t+4)^3} / 27 [/tex] evaluated from 0 to 1

Is my approach correct, and if so, should I just keep these integrals on hand, or do I need to memorize all those forms?

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# Homework Help: Length of a curve problem

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