MATH 1552 Chapter : C2 Arclength
Document Summary
A parametric equation for a circle of radius 1 and center (0, 0) is: x = cos t, y = sin t . The equations x = f (t), y = g(t) are called parametric equations. Given a parametric curve, sometimes we can eliminate t and obtain an equivalent non-parametric equation for the same curve. Example: find a non-parametric equation for the following para- metric curve: x = t2 2t, y = t + 1 . Here we describe how to nd the length of a smooth arc. A smooth arc is the graph of a continuous function whose derivative is also continuous (so it does not have corner points). If the arc is just a straight line between two points of coordinates (x1, y1), (x2, y2), its length can be found by the pythagorean theorem: where x = x2 x1 and y = y2 y1.
