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| Arc Length of a Parametric Curve |
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Parametric Equations Because the graph in the xy-plane of a function f can be cut at most once by any vertical line, there are many important curves in the xy-plane that are not graphs of equations of the form y=f(x) . Imagine a particle moving along a curve C in the xy-plane, the x- and y- coordinates of the particle are functions of time, say x=f(t) , y=g(t) Lets sketch the trajectory over time interval 0<=t<=4 of the particle that moves in the xy-plane with the equations of motion  , 
The physicists' concept of equations of motion has been adapted by
mathematicians to describe curves in the xy-plane by pairs of equations x=x(t)
y=y(t) that express the coordinates (x,y) of a point on a curve as
functions of an auxiliary variable t called parameter and the
equations are called parametric equations for the curve.
The parameter t may not represent time, it should be taken as an
independent variable that varies over some interval of real numbers. If
not restrictions on t are stated explicitly then it is understood that t
varies between Finding Arc Length of Curves defined parametrically. Using this formula to compute the arc length of the function defined
above gives an answer of 26.18 |
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Related Topic
How to compute Arc Length (Rectangular) |
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