Mathematics, 07.03.2020 05:17 carlinryan
A lamina occupies the part of the disk x2+y2≤4 in the top half. Find its mass if the density at any point is 2.3 times the point's distance from the origin.
Answers: 1
![m=\int\limits^a_b \int\limits^a_b {\rho} dA\\\\m=\int\limits^{2\pi }_{\pi}\int\limits^2_0 {2.3r^2.r} \, drd\theta\\\\m=2.3\int\limits^{2\pi }_{\pi} \, d\theta\int\limits^2_0 {r^3} \, dr\\\\m=2.3[\theta]_{\pi}^{2\pi}\times [\dfrac{r^4}{4}]_2^0\\\\m=\dfrac{2.3}{4}(2\pi-\pi)(16-0)\\\\m=\dfrac{2.3\pi}{4}\times 16\\\\m=2.3\times 4=9.2](/tpl/images/0537/9104/6c356.png)
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A lamina occupies the part of the disk x2+y2≤4 in the top half. Find its mass if the density at any...
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