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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 $.

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Calculus 2 / BC

Chapter 8

Further Applications of Integration

Section 3

Applications to Physics and Engineering

Applications of Integration

Oregon State University

Harvey Mudd College

Baylor University

Boston College

Lectures

01:09

The centroid of a curve ca…

03:44

The centroid of curve can …

01:39

Let $\mathscr{R}$ be the r…

01:05

Let $C$ be a simple curve …

Let $\mathscr{H}$ be the r…

04:31

Most centroid calculations…

10:10

03:29

Centroid of unbounded regi…

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