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O Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. x=6√ 3y, x = 0, y = 3; about the y-axis V= Sketch the region. 15 10 сл y y y y 3.0 3.0- 15 2.5 2.5 2.0 2.0 10 10 1.5 1.5 X 0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0 Sketch the solid and a typical disk or washer. Need Help? X 1.0 0.5 X ⑪O 5 10 15 O Interactive 3D Graph Help Interactive 3D Graph Help 20 5 4 3 2 1 -1-2-3-4-5 10 -201 20 10 O 1.0 0.5 Interactive 3D Graph Help -5 -4 -3 -2 -1 T 4 5 -20 -10 10 -2 -20 -5 20 20 X 5 10 15 Interactive 3D Graph Help -20 -10 5 3 4 2 1 -5 10 20 Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y=x+1, y = 0, x = 0, x = 5; about the x-axis V I Sketch the region. y 가 6 Сл حر 3 2 1 1 2 3 5 сл Sketch the solid and a typical disk or washer. O Interactive 3D Graph <-10 -5 10 5 -5 10 6 y y y 가 6 6 5 5 5 4 3 4 2 X X 1 2 3 4 5 6 5 10 10 3 2- 1 3 2 X 1 2 3 4 5 6 1 2 Help Interactive 3D Graph Help Interactive 3D Graph →Help y 10 10 10 Interactive 3D Graph Help -10 -5 10 5 -5 10 + -10 -5 S -5 5 10 10 -10 -5 5 -10 +x 10 10 3 5 Сл 6 X

O Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. x=6√ 3y, x = 0, y = 3; about the y-axis V= Sketch the region. 15 10 сл y y y y 3.0 3.0- 15 2.5 2.5 2.0 2.0 10 10 1.5 1.5 X 0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0 Sketch the solid and a typical disk or washer. Need Help? X 1.0 0.5 X ⑪O 5 10 15 O Interactive 3D Graph Help Interactive 3D Graph Help 20 5 4 3 2 1 -1-2-3-4-5 10 -201 20 10 O 1.0 0.5 Interactive 3D Graph Help -5 -4 -3 -2 -1 T 4 5 -20 -10 10 -2 -20 -5 20 20 X 5 10 15 Interactive 3D Graph Help -20 -10 5 3 4 2 1 -5 10 20 Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y=x+1, y = 0, x = 0, x = 5; about the x-axis V I Sketch the region. y 가 6 Сл حر 3 2 1 1 2 3 5 сл Sketch the solid and a typical disk or washer. O Interactive 3D Graph <-10 -5 10 5 -5 10 6 y y y 가 6 6 5 5 5 4 3 4 2 X X 1 2 3 4 5 6 5 10 10 3 2- 1 3 2 X 1 2 3 4 5 6 1 2 Help Interactive 3D Graph Help Interactive 3D Graph →Help y 10 10 10 Interactive 3D Graph Help -10 -5 10 5 -5 10 + -10 -5 S -5 5 10 10 -10 -5 5 -10 +x 10 10 3 5 Сл 6 X

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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O Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. x=6√ 3y, x = 0, y = 3; about the y-axis V= Sketch the region. 15 10 сл y y y y 3.0 3.0- 15 2.5 2.5 2.0 2.0 10 10 1.5 1.5 X 0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0 Sketch the solid and a typical disk or washer. Need Help? X 1.0 0.5 X ⑪O 5 10 15 O Interactive 3D Graph Help Interactive 3D Graph Help 20 5 4 3 2 1 -1-2-3-4-5 10 -201 20 10 O 1.0 0.5 Interactive 3D Graph Help -5 -4 -3 -2 -1 T 4 5 -20 -10 10 -2 -20 -5 20 20 X 5 10 15 Interactive 3D Graph Help -20 -10 5 3 4 2 1 -5 10 20
Transcribed Image Text:O Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. x=6√ 3y, x = 0, y = 3; about the y-axis V= Sketch the region. 15 10 сл y y y y 3.0 3.0- 15 2.5 2.5 2.0 2.0 10 10 1.5 1.5 X 0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0 Sketch the solid and a typical disk or washer. Need Help? X 1.0 0.5 X ⑪O 5 10 15 O Interactive 3D Graph Help Interactive 3D Graph Help 20 5 4 3 2 1 -1-2-3-4-5 10 -201 20 10 O 1.0 0.5 Interactive 3D Graph Help -5 -4 -3 -2 -1 T 4 5 -20 -10 10 -2 -20 -5 20 20 X 5 10 15 Interactive 3D Graph Help -20 -10 5 3 4 2 1 -5 10 20
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y=x+1, y = 0, x = 0, x = 5; about the x-axis V I Sketch the region. y 가 6 Сл حر 3 2 1 1 2 3 5 сл Sketch the solid and a typical disk or washer. O Interactive 3D Graph <-10 -5 10 5 -5 10 6 y y y 가 6 6 5 5 5 4 3 4 2 X X 1 2 3 4 5 6 5 10 10 3 2- 1 3 2 X 1 2 3 4 5 6 1 2 Help Interactive 3D Graph Help Interactive 3D Graph →Help y 10 10 10 Interactive 3D Graph Help -10 -5 10 5 -5 10 + -10 -5 S -5 5 10 10 -10 -5 5 -10 +x 10 10 3 5 Сл 6 X
Transcribed Image Text:Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y=x+1, y = 0, x = 0, x = 5; about the x-axis V I Sketch the region. y 가 6 Сл حر 3 2 1 1 2 3 5 сл Sketch the solid and a typical disk or washer. O Interactive 3D Graph <-10 -5 10 5 -5 10 6 y y y 가 6 6 5 5 5 4 3 4 2 X X 1 2 3 4 5 6 5 10 10 3 2- 1 3 2 X 1 2 3 4 5 6 1 2 Help Interactive 3D Graph Help Interactive 3D Graph →Help y 10 10 10 Interactive 3D Graph Help -10 -5 10 5 -5 10 + -10 -5 S -5 5 10 10 -10 -5 5 -10 +x 10 10 3 5 Сл 6 X
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