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If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
Section 8.3 : Center Of Mass
Find the center of mass for each of the following regions.
- The region bounded by \(y = {x^3}\) , \(x = - 2\) and the \(x\)-axis.
- The triangle with vertices \((-2, -2)\), \((4, -2)\) and \((4,4)\).
- The region bounded by \(y = {\left( {x - 2} \right)^2}\) and \(y = 4\).
- The region bounded by \(y = \cos \left( x \right)\) and the x-axis between \(\displaystyle - \frac{\pi }{2} \le x \le \frac{\pi }{2}\).
- The region bounded by \(y = {x^2}\) and \(y = 6 - x\).
- The region bounded by \(y = {{\bf{e}}^{2x}}\) and the x-axis between \( - 1 \le x \le 1\).
- The region bounded by \(y = {{\bf{e}}^{2x}}\) and \(y = - \cos \left( {\pi x} \right)\) between \(\displaystyle - \frac{1}{2} \le x \le \frac{1}{2}\).