91Ó°ÊÓ

For the following exercises, calculate the center of mass for the collection of masses given. $$ m_{1}=1 \text { at }(1,0) \text { and } m_{2}=3 \text { at }(2,2) $$

For the following exercises, compute the center of mass \((\bar{x}, \bar{y})\). Use symmetry to help locate the center of mass whenever possible. $$ \rho=7 \text { in the square } 0 \leq x \leq 1, \quad 0 \leq y \leq 1 $$

For the following exercises, compute the center of mass \((\bar{x}, \bar{y})\). Use symmetry to help locate the center of mass whenever possible. \(\rho=3\) in the triangle with vertices \((0,0), \quad(a, 0),\) and \((0, b)\)

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

For the following exercises, use a calculator to draw the region, then compute the center of mass \((\bar{x}, \bar{y})\). Use symmetry to help locate the center of mass whenever possible. [T] The region bounded by \(y=\cos (2 x)\), \(x=-\frac{\pi}{4},\) and \(x=\frac{\pi}{4}\)

For the following exercises, use a calculator to draw the region, then compute the center of mass \((\bar{x}, \bar{y})\). Use symmetry to help locate the center of mass whenever possible. [T] The region between \(y=2 x^{2}, \quad y=0, \quad x=0\), and \(x=1\)

For the following exercises, use a calculator to draw the region, then compute the center of mass \((\bar{x}, \bar{y})\). Use symmetry to help locate the center of mass whenever possible. [T] Region between \(y=\sqrt{x}, \quad y=\ln (x), \quad x=1\), and \(x=4\)

For the following exercises, use a calculator to draw the region, then compute the center of mass \((\bar{x}, \bar{y})\). Use symmetry to help locate the center of mass whenever possible. [T] The region bounded by \(y=0, \quad \frac{x^{2}}{4}+\frac{y^{2}}{9}=1\)

For the following exercises, use a calculator to draw the region, then compute the center of mass \((\bar{x}, \bar{y})\). Use symmetry to help locate the center of mass whenever possible. [T] The region bounded by \(y=0, \quad x=0\), and \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\)

For the following exercises, use a calculator to draw the region, then compute the center of mass \((\bar{x}, \bar{y})\). Use symmetry to help locate the center of mass whenever possible. [T] The region bounded by \(y=x^{2}\) and \(y=x^{4}\) in the first quadrant