Parametric and Polar Curves

Problem : Find the length of the parametric curve given by

,(2t + 1)3/2

Solution for Problem 1 >>

The length formula gives

dt	=	dt
		= t + 1dt
	= + x	= 4

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Problem : Compute the length of (t + sin(t), 2 - cos(t)) from t = 0 to 3Π . You may use the trigonometric identity 1 + cos(θ) = 2 cos²(θ/2).

Solution for Problem 2 >>

The velocity vector of this parametric curve at time t equals (1 + cos(t), sin(t)) , so the length of the curve is

dt	=
	=	dt
	=	2 cos dt
	=	2cos dt + 2 - cos dt
	=	22 sin +2 -2 sin
	=	12.

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