54. Sketch the region in the xy-plane defined by the inequalities x - 2y²0, 1- x - y| ≥ 0 and find its area.

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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For clarification on this problem, why would evaluating the integral from [−1/2,1/2] not suffice compared to how it was solved per the solution of using the symmetric method: [0,1/2] and then multiplying the integral by 2? I tried evaluating the integral (1-y-2y^2)dy from [-1/2, 1/2] but not arriving to the answer: 7/12, which is solution evaluating from [0,1/2] and multiply the integral by 2.

54. Sketch the region in the xy-plane defined by the inequalities
-
x – 2y² ≥ 0, 1 − x − |y| ≥ 0 and find its area.
Transcribed Image Text:54. Sketch the region in the xy-plane defined by the inequalities - x – 2y² ≥ 0, 1 − x − |y| ≥ 0 and find its area.
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