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For the following exercises, use a calculator to draw the region enclosed by the curve. Find the area $M$ and the centroid $(\overline{x}, \overline{y})$ for the given shapes. Use symmetry to help locate the center of mass whenever possible.Half-ring: $\quad y^{2}+x^{2}=1, \quad y^{2}+x^{2}=4, \quad$ and $y=0$

$(\overline{x}, \overline{y})=\left(0, \frac{28}{9 \pi}\right)$$M=\frac{3 \pi}{2}$ units $^{2}$

Calculus 2 / BC

Chapter 6

Applications of Integration

Section 6

Moments and Centers of Mass

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

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The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

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