For the following exercises, draw the region bounded by the curves. Then, find the volume when the region is rotated around the y-axis.

x=sec (y) and \(y=\frac{\pi}{4}\), y=0 and x=0

Text Transcription:

y=pi/4

× ⃗⃗1⃗⃗2⃗⃗⃗3⃗ } ⃗3⃗ 2⃗⃗ ⃗1⃗⃗ ⃗3⃗⃗ = 1 1⃗⃗ +2 2⃗⃗⃗ 1⃗⃗2⃗⃗3⃗ } ⃗1⃗⃗2⃗⃗ } ⃗1⃗⃗2⃗ } = { , ,…, } ⃗⃗⃗⃗ 1 2 = 1 1 2 2⋯+ ⃗⃗ 1,2,…, ⃗ 1 [] = [ ] ⋮ ↦ [ ] ↦ => 3 −1 1= [6],2= [0 ] 2 1 3 −1 = {6 ] [0 ]} 2 1 ⃗ = ⃗ ( − ) 3. det( − ) = 0 1 3 −5 [0 2 4 ] 0 0