© 2016 Shmoop University, Inc. All rights reserved.
Area, Volume, and Arc Length
Arc Length for Parametric Functions Exercises
Write an integral expression for the length of the curve described by the parametric equations
x( t) = e and t y( t) = 2 t + 1 for 0 ≤ t ≤ 4.
x( t) = cos t and y( t) = 2sin t describe a parametric curve.
(a) Write an integral expression for the length of the portion of the curve graphed below.
(b) Use a calculator to evaluate your integral and explain why your answer is reasonable.
Write an integral expression for the parametric function described by the equations
x( t) = x 3 y( t) = esin t t
for 0 ≤
t ≤ π.
Write an integral expression for the length of the parametric curve
x = t cos t y = t sin t
α ≤ t ≤ β. Use the equality sin 2 t + cos 2 t = 1 to simplify your expression. (It will still be an integral.)