Mathematics, 29.07.2020 01:01 angelearlyp9ynm9
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.? y = 2 + sec(x), −π/3 ≤ x ≤ π/3, y = 4; about y = 2
Answers: 3
![\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}](/tpl/images/0714/4518/e477b.png)
![V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(4-2)^2 - (2+ sec \ x -2)^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(2)^2 - (sec \ x )^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [4 - sec^2 \ x ]dx](/tpl/images/0714/4518/c76a1.png)
![V = \pi [4x - tan \ x]^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) - 4(-\dfrac{\pi}{3})+ tan (-\dfrac{\pi}{3})] \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) + 4(\dfrac{\pi}{3})- tan (\dfrac{\pi}{3})] \\ \\ \\ V = \pi [8(\dfrac{\pi}{3}) - 2 \ tan (\dfrac{\pi}{3}) ]](/tpl/images/0714/4518/d6799.png)
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