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**Lengths of Plane Curves**

6.3 Lengths of Plane Curves

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**Length of a parametrically defined curve**

Lk the line segment between Pk and Pk-1

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**Example 1 The circumference of a circle**

Find the length of the circle of radius r defined parametrically by x=r cos t and y=r sin t, 0 ≤ t ≤ 2p

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**Length of a curve y = f(x)**

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**Example 3 Applying the arc length formula for a graph**

Find the length of the curve

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**Dealing with discontinuity in dy/dx**

At a point on a curve where dy/dx fails to exist and we may be able to find the curve’s length by expressing x as a function of y and applying the following

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**Example 4 Length of a graph which has a discontinuity in dy/dx**

Find the length of the curve y = (x/2)2/3 from x = 0 to x = 2. Solution dy/dx = (1/3) (2/x)1/3 is not defined at x=0. dx/dy = 3y1/2 is continuous on [0,1].

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