
# 9.9: Arc Length

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Here is another geometric application of the integral: find the length of a portion of a curve. As usual, we need to think about how we might approximate the length, and turn the approximation into an integral.

We already know how to compute one simple arc length, that of a line segment. If the endpoints are $$P_0(x_0,y_0)$$ and $$P_1(x_1,y_1)$$ then the length of the segment is the distance between the points, $$\sqrt{(x_1-x_0)^2+(y_1-y_0)^2}$$, from the Pythagorean theorem, as illustrated in Figure $$\PageIndex{1}$$.

### Contributors

• Integrated by Justin Marshall.