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Homework Statement
Find the length of the curve r = cos(θ) - sin(θ), 0<θ<∏/4
Homework Equations
L=∫ds
ds=sqrt(r^2 + (dr/dθ)^2)
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?