Explanation 1) Concept: Graph the two curves, and set up the integral for area between two curves. The region is bounded by the curves with equations x = f y , x = g y between y = c and y = d , where f and g are continuous. Then area is A = ∫ c d | f y - g y | d y 2) Given: The inequalities x - 2 y 2 > 0 , 1 - x - | y | > 0 4) Calculation: The inequality x > 2 y 2 describes the region that lies on or to the right side of the parabola x = 2 y 2 , and the inequality x < 1 - | y | describes the region that lies on the left of the curve x = 1 - | y | . 1 - y = 1 - y i f y ≥ 0 y - 1 i f y < 0 The sketch of the region

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ISBN: 9781305266698

Author: James Stewart

Publisher: Cenage Learning

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Chapter 5.1, Problem 46E

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The regions defined by the given inequalities and find its area

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Chapter 5.1, Problem 45E

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Chapter 5 Solutions

Calculus 8th Edition

Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Prob. 3E Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Prob. 10E

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The regions defined by the given inequalities and find its area

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To sketch:

The regions defined by the given inequalities and find its area