Arc Length of Curves
Let y = f(x) represent a smooth curve on the interval [a, b], as shown in Figure 1. The arc length S of the curve f(x) between x = a and x = b is
Example 1 Find the arc length of the curvefrom x = 0 to x = 3, and use the GraphFunc utility online to verify the result.
Using yields a length of
Use GraphFunc utility online to verify the above result as shown in the following steps:
We see that the arc lengths that GraphFunc computes and the one we derive are the same.
Example 2 Find the arc length of the curve y = ln(cos x) from x = 0 to and use the GraphFunc utitlity online to confirm the result.
We use GraphFunc utility online and follow the steps indicated in the Example 1 to plot the graph and compute the arc length The result is illustrated in Figure 3.
Now you try to use the GraphFunc utility to compute the arc lengths of your graphs online.
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