Explanation Given: The figure is: The functions are y = 2 − x 2 and y = x . Formula used: Area of the region A = ∫ a b [ ( Upper function ) − ( Lower function ) ] d x Where a ≤ x ≤ b Calculation: The functions are y = 2 − x 2 and y = x . The graphs of y = 2 − x 2 and y = x intersect where 2 − x 2 = x x 2 + x − 2 = 0 Find the factors of the above equation. x 2 + 2 x − x − 2 = 0 x ( x + 2 ) − 1 ( x + 2 ) = 0 ( x + 2 ) ( x − 1 ) = 0 That is. ( x + 2 ) = 0 or ( x − 1 ) = 0 x = − 2 or x = 1 Thus, the enclosed area lies over the interval [ − 2 , 1 ] . The region enclosed by the graphs lies above y = 2 − x 2 and below y = x over the interval [ − 2 , 1 ] . Now, find the area...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6, Problem 2CRE

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Compute the area of the region in Figure 1(B) enclosed by $y = 2 - x^{2}$ and $y = x$ .

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Chapter 6, Problem 1CRE

Chapter 6, Problem 3CRE

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Chapter 6 Solutions

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Compute the area of the region in Figure 1(B) enclosed by y = 2 − x 2 and y = x .

Solution Summary: The author calculates the area of the region in Figure 1(B) enclosed by the functions y = 2 x 2

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Compute the area of the region in Figure 1(B) enclosed by $y = 2 - x^{2}$ and $y = x$ .

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Chapter 6 Solutions

Compute the area of the region in Figure 1(B) enclosed by y = 2 − x 2 and y = x .

Solution Summary: The author calculates the area of the region in Figure 1(B) enclosed by the functions y = 2 x 2

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Compute the area of the region in Figure 1(B) enclosed by y=2−x2 and y=x.

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Chapter 6 Solutions

Compute the area of the region in Figure 1(B) enclosed by $y = 2 - x^{2}$ and $y = x$ .