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For the following exercises, compute the center of mass $(\overline{x}, \overline{y}) .$ Use symmetry to help locate the center of mass whenever possible.$$\begin{array}{l}{ \rho=2 \text { for the region bounded by } y=\cos (x)} \\ {y=-\cos (x), \quad x=-\frac{\pi}{2}, \text { and } x=\frac{\pi}{2}}\end{array}$$

$(0,0)$

Calculus 2 / BC

Chapter 6

Applications of Integration

Section 6

Moments and Centers of Mass

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Okay, so we have that y is equal to co sign a Becks. And why people to negative post in a box. And this is between ex being negative fire before or part of a tutu. However, so are grass looks something like this. So this is some pie over too. I'm gonna have to fire with Chip. So then it is something like this. That's co sign of exit. This is negative. Close side of ex. Okay, Were asked to you something to help locate sense of mass whatever possible. Well, if you recall since co sign of X or actually, yeah. If we reflect coastline of X across the X axis, it just becomes negative posts on our backs. So our top portion and are bottom portion are so much. So based on this, we could know that if our action, if we know that they are sick, the magic across both the x and y axis, then our center of mass is just a origin. And in this case, origin is Darryl comments. So

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