Mathematics, 20.07.2019 22:10 organicmemez
Evaluate x2 dv, e where e is the solid that lies within the cylinder x2 + y2 = 4, above the plane z = 0, and below the cone z2 = 9x2 + 9y2.
Answers: 1
wherein E is indeed the solid that exists inside the cylinders 
 above surface 
, that is below the cones 
 E's precession through into xy-plane is 
 with 
in![[0,2 \pi ] \\\\](/tpl/images/0113/2395/67c40.png)
![=\int^{2\pi}_{0} \int^{2}_{0}\int^{3r}_{z= 0} r^3 \cos^2 \theta \ dz \ dr \ d\theta \\\\= \int^{2\pi}_{0} \int^{2}_{0} 3r^4 \cos^2 \theta \ dr \ d\theta \\\\= 3 \int^{2\pi}_{0} \frac{1}{2} \frac{2^5}{5}(1+\cos\ 2 \theta) \ d\theta \\\\= \frac{48}{5}[ (\theta +\frac{1}{2}\sin 2 \theta) ]^{2\pi}_{0} \\\\= \frac{96\pi}{5}](/tpl/images/0113/2395/3edf2.png)
" .![\begin{cases}x=r\cos t\\y=r\sin t\\z=z\end{cases]](/tpl/images/0113/2395/a82cf.png)
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Evaluate x2 dv, e where e is the solid that lies within the cylinder x2 + y2 = 4, above the plane z...
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