CALCULUS Understanding Its Concepts and Methods

Arc length

The arc length
of the parametric curve (*x*(*t*),* y*(*t*)),
for *t* between *a*
and *b*, is given by

The arc length
of the rectangular graph of *y = f*(*t*)
, for *x * between
*a*
and *b*, is

The arc length
of the polar graph of *r = f*(*q* ), for *q* between *a*
and *b*, is

The arc length
of the parametric curve (*x*(*t*),* y*(*t*),*
z*(*t*)), for *t * between
*a*
and *b*, is given by

Arc length can be approximated by adding
together the lengths of line segments joining points on the curve,
as suggested in the figure.

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.