Mathematics, 12.08.2020 08:01 Description
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. y = 6x − x2, y = 8; about x = 2
Answers: 3
![\mathbf{V = [\dfrac{ 8 \pi }{3}] }](/tpl/images/0719/9373/06eb4.png)
![V = 2 \pi [\dfrac{ -x^7}{4}+\dfrac{8x^3}{3} -\dfrac{20x^2}{2} +16x]^4_2](/tpl/images/0719/9373/fb263.png)
![V = 2 \pi [\dfrac{ -(4^4-2^4)}{4}+\dfrac{8(4^3-2^3)}{3} -\dfrac{20(4^2-2^2)}{2} +16(4-2) ]^4_2](/tpl/images/0719/9373/f132c.png)
![V = 2 \pi [\dfrac{ -(256-16)}{4}+\dfrac{8(64-8)}{3} -10(16-4)} +16(2) ]](/tpl/images/0719/9373/115b5.png)
![V = 2 \pi [\dfrac{ 4}{3}]](/tpl/images/0719/9373/c0454.png)
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Use the method of cylindrical shells to find the volume V generated by rotating the region bounded b...
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