Can you plese explain step by step how to answer these Q? 1) Three regions are defined in the figure. The x y coordinate plane is given. A rectangle containing a line, a curve, and three shaded regions is on the graph. The rectangle is formed by the origin, point A (1, 0), point B (1, 3), and point C (0, 3). The line y = 3x begins at the origin, goes up and right, and ends at point B (1, 3). The curve y = 3∜x begins at the origin, goes up and right becoming less steep, and ends at point B (1, 3). Region R1 is below the line, above the x-axis and left of the line segment A B. Region R2 is above the curve, right of the y-axis and below the line segment B C. Region R3 is below the curve and above the line. Find the volume generated by rotating the given region about the specified line. ℛ1 about O A 2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Can you plese explain step by step how to answer these Q?

1)

Three regions are defined in the figure.
The x y coordinate plane is given. A rectangle containing a line, a curve, and three shaded regions is on the graph.
  • The rectangle is formed by the origin, point A (1, 0), point B (1, 3), and point C (0, 3).
  • The line y = 3x begins at the origin, goes up and right, and ends at point B (1, 3).
  • The curve y = 3∜x begins at the origin, goes up and right becoming less steep, and ends at point B (1, 3).
  • Region R1 is below the line, above the x-axis and left of the line segment A B.
  • Region R2 is above the curve, right of the y-axis and below the line segment B C.
  • Region R3 is below the curve and above the line.
Find the volume generated by rotating the given region about the specified line.
1 about O A
2) 
Three regions are defined in the figure.
C (0,3
y
R₂
y=3√√x
y = 3x
R₁
B(1,3)
A (1,0)
X
Find the volume generated by rotating the given region about the specified line.
R1 about OA
Transcribed Image Text:Three regions are defined in the figure. C (0,3 y R₂ y=3√√x y = 3x R₁ B(1,3) A (1,0) X Find the volume generated by rotating the given region about the specified line. R1 about OA
Three regions are defined in the figure.
y
C (0, 2)
0
R₂
/y = 2√√x
R3
y = 2 x
R₁
B(1,2)
A (1,0)
X
Find the volume generated by rotating the given region about the specified line.
R3 about OC
Transcribed Image Text:Three regions are defined in the figure. y C (0, 2) 0 R₂ /y = 2√√x R3 y = 2 x R₁ B(1,2) A (1,0) X Find the volume generated by rotating the given region about the specified line. R3 about OC
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