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# The centroid of a $curve$ can be found by a process similar to the one we used for finding the centroid of a region. If $C$ is a curve with length $L$, then the centroid is $(\bar{x}, \bar{y})$ where $\bar{x} = (\frac{1}{L}) \int x\ ds$ and $\bar{y} = (\frac{1}{L}) \int y\ ds$. Here we assign appropriate limits of integration, and $ds$ is as defined in Sections 8.1 and 8.2. ( The centroid often doesn't lie on the curve itself. If the curve were made of wire and placed on a weightless board, the centroid would be the balance point on the board.) Find the centroid of the quarter-circle $y = \sqrt{16 - x^2}$, $0 \le x \le 4$.

## $\bar{x}=8 / \pi, \bar{y}=3 / \pi$

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Applications of Integration

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### Video Transcript

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Applications of Integration

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