Mathematics, 24.07.2019 20:00 3076850
The region bounded by the given curve is rotated about the specified axis. find the volume v of the resulting solid by any method. x2 + (y − 4)2 = 16; about the y-axis
Answers: 1
![\bf \displaystyle \pi \int\limits_{0}^8~8y\cdot dy - \pi \int\limits_{0}^8~y^2\cdot dy\implies \pi \left[ 4y^2~-~\cfrac{y^3}{3} \right]_{0}^8 \\\\\\ \pi \left[ \left[ 256-\cfrac{51}{3} \right]~-~[0] \right]\implies \pi \cdot \cfrac{256}{3}\implies \cfrac{256\pi }{3}\implies 85\frac{\pi }{3}](/tpl/images/0128/4328/1338a.png)
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