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3. Let R be the region bounded by the curves C1 : y – 3 = -2(x – 1)², C2 : x + y = 4, and C3 : y = 1. y (1,3) (0,1) (3,1) Set up (but do not evaluate) a definite integral or sum of definite integrals that is equal to the following. a. Area of R using vertical rectangles b. Length of the boundary of R along C1 c. Volume of the solid generated when R is revolved about the line x = 4. d. Volume of the solid whose base is R and whose cross-sections perpendicular to the y-axis are squares.

3. Let R be the region bounded by the curves C1 : y – 3 = -2(x – 1)², C2 : x + y = 4, and C3 : y = 1. y (1,3) (0,1) (3,1) Set up (but do not evaluate) a definite integral or sum of definite integrals that is equal to the following. a. Area of R using vertical rectangles b. Length of the boundary of R along C1 c. Volume of the solid generated when R is revolved about the line x = 4. d. Volume of the solid whose base is R and whose cross-sections perpendicular to the y-axis are squares.

Algebra & Trigonometry with Analytic Geometry
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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3. Let R be the region bounded by the curves C1 : y – 3 = -2(x – 1)², C2 : x + y = 4, and C3 : y = 1. y (1,3) (0,1) (3,1) Set up (but do not evaluate) a definite integral or sum of definite integrals that is equal to the following. a. Area of R using vertical rectangles b. Length of the boundary of R along C1 c. Volume of the solid generated when R is revolved about the line x = 4. d. Volume of the solid whose base is R and whose cross-sections perpendicular to the y-axis are squares.
Transcribed Image Text:3. Let R be the region bounded by the curves C1 : y – 3 = -2(x – 1)², C2 : x + y = 4, and C3 : y = 1. y (1,3) (0,1) (3,1) Set up (but do not evaluate) a definite integral or sum of definite integrals that is equal to the following. a. Area of R using vertical rectangles b. Length of the boundary of R along C1 c. Volume of the solid generated when R is revolved about the line x = 4. d. Volume of the solid whose base is R and whose cross-sections perpendicular to the y-axis are squares.
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