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The length of the curve r = cos(θ) - sin(θ), 0<θ<∏/4

  1. May 19, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the length of the curve r = cos(θ) - sin(θ), 0<θ<∏/4

    2. Relevant equations

    L=∫ds
    ds=sqrt(r^2 + (dr/dθ)^2)

    3. The attempt at a solution

    r^2 = (cosθ - sinθ)^2 = cos^2(θ) -2cosθsinθ + sin^2(θ) =1-2cosθsinθ

    dr/dθ = -sinθ -cosθ

    (dr/dθ)^2 = 1+2cosθsinθ

    L=∫sqrt(2)dθ=sqrt(2)[θ]=sqrt(2) [pi/4]

    But the answer is pi/(2*sqrt(2)). Where did I go wrong?
     
  2. jcsd
  3. May 19, 2014 #2

    jbunniii

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    Science Advisor
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    Gold Member

    You didn't. The two answers are the same, just written differently:
    $$\frac{\sqrt{2} \pi}{4} = \frac{\sqrt{2} \pi}{4} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{2\pi}{4 \sqrt{2}} = \frac{\pi}{2 \sqrt{2}}$$
     
  4. May 19, 2014 #3
    Thanks!
     
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