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Activity 6.1.3. In each of the following problems, our goal is to determine the area of the region described. For each region, (i) determine the intersection points of the curves, (ii) sketch the region whose area is being found, (iii) draw and label a repre- sentative slice, and (iv) state the area of the representative slice. Then, state a defi- nite integral whose value is the exact area of the region, and evaluate the integral to find the numeric value of the region's area. Note well: At the step where you draw a representative slice, you need to make a choice about whether to slice vertically or horizontally. = 6-2y². a. The finite region bounded by x = y² and x = b. The finite region bounded by x = 1 - y² and x = 2-2y².

Activity 6.1.3. In each of the following problems, our goal is to determine the area of the region described. For each region, (i) determine the intersection points of the curves, (ii) sketch the region whose area is being found, (iii) draw and label a repre- sentative slice, and (iv) state the area of the representative slice. Then, state a defi- nite integral whose value is the exact area of the region, and evaluate the integral to find the numeric value of the region's area. Note well: At the step where you draw a representative slice, you need to make a choice about whether to slice vertically or horizontally. = 6-2y². a. The finite region bounded by x = y² and x = b. The finite region bounded by x = 1 - y² and x = 2-2y².

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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Activity 6.1.3. In each of the following problems, our goal is to determine the area of the region described. For each region, (i) determine the intersection points of the curves, (ii) sketch the region whose area is being found, (iii) draw and label a repre- sentative slice, and (iv) state the area of the representative slice. Then, state a defi- nite integral whose value is the exact area of the region, and evaluate the integral to find the numeric value of the region's area. Note well: At the step where you draw a representative slice, you need to make a choice about whether to slice vertically or horizontally. a. The finite region bounded by x = y² and x = y² and x = 6 - 2y². b. The finite region bounded by x = 1 - y² and x = 2 – 2y².
Transcribed Image Text:Activity 6.1.3. In each of the following problems, our goal is to determine the area of the region described. For each region, (i) determine the intersection points of the curves, (ii) sketch the region whose area is being found, (iii) draw and label a repre- sentative slice, and (iv) state the area of the representative slice. Then, state a defi- nite integral whose value is the exact area of the region, and evaluate the integral to find the numeric value of the region's area. Note well: At the step where you draw a representative slice, you need to make a choice about whether to slice vertically or horizontally. a. The finite region bounded by x = y² and x = y² and x = 6 - 2y². b. The finite region bounded by x = 1 - y² and x = 2 – 2y².
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