Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 2 sin(x), y = 2 cos(x), 0≤x≤ */4; about y = -1 V=

Calculus: Early Transcendentals
8th Edition
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Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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question 10 on 6.2

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = 2 sin(x), y = 2 cos(x), 0≤x≤ x/4; about y = -1
V =
Sketch the region.
-0.5
-1.5
1
-1.0 -0.5
-0.4 -0.2
-0.4 -0.2
3
0.5
Sketch the solid, and a typical disk or washer.
y
2
y
2
1
1,0
0.5
1.5
1.0
0.2 0.4 0.6 0.8 1.0
0.2 0.4 0.6 0.8 1.0
X
X
-0.4 -0.2
-0.4 -0.2
-0.4 -0.2
-0.4 -0.2
y
1
1
y
0.2 0.4 0.6 0.8 1.0
0.2 0.4 0.6 0.8 1.0
0.2 0.4 0.6 0.8 1.0
0.2 0.4 0.6 0.8 1.0
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 = 2 sin(x), y = 2 cos(x), 0≤x≤ x/4; about y = -1 V = Sketch the region. -0.5 -1.5 1 -1.0 -0.5 -0.4 -0.2 -0.4 -0.2 3 0.5 Sketch the solid, and a typical disk or washer. y 2 y 2 1 1,0 0.5 1.5 1.0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 X X -0.4 -0.2 -0.4 -0.2 -0.4 -0.2 -0.4 -0.2 y 1 1 y 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0
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