Mathematics, 11.11.2019 09:31, 22emilyl530
Find the exact coordinates of the centroid for the region bounded by the curves y=x, y=1/x, y=0, and x=2
Answers: 2
![A = \int_{1}^{2} \, (x- \frac{1}{x})dx =[ \frac{x^{2}}{2}-ln(x)]_{1}^{2} = \frac{3}{2}-ln(2) =0. 8069](/tpl/images/0368/9035/66678.png)
![0.8069x_{1} = \int_{1}^{2} x(x- \frac{1}{x})dx =[ \frac{x^{3}}{3}-x]_{1}^{2} = \frac{7}{3}-1= 1.3333\\x_{1} =1.6524](/tpl/images/0368/9035/fa286.png)
![0.8069y_{1} = \int_{1/2}^{1} y(2- \frac{1}{y} )dy + \int_{1}^{2} y(2-y)dy \\ = [y^{2}-y]_{1/2}^{1} + [y^{2}- \frac{y^{3}}{3}]_{1}^{2} =0.9167 \\ y_{1} =1.1361](/tpl/images/0368/9035/21f00.png)
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Find the exact coordinates of the centroid for the region bounded by the curves y=x, y=1/x, y=0, and...
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