Explanation 1) Concept: The area A of the region bounded by the curves y = f ( x ) , y = g ( x ) and the lines x = a a n d x = b is A = ∫ a b f x - g x d x f x - g x = f x - g x w h e n f x ≥ g ( x ) g x - f x w h e n g x ≥ f ( x ) 2) Given: y = x x 2 + 1 2 , y = x 5 - x , x ≥ 0 3) Calculation: f x = x x 2 + 1 2 and g x = x 5 - x i) To find the intersection point of the curves, draw the graph. From the sketch, it is clear that the curves intersect at x = 0 and x = 1.052 ii) the upper curve is y = x x 2 + 1 2 and the lower curve is y = x 5 - x Therefore, A = ∫ 0 1.052 x x 2 + 1 2 - ( x 5 - x ) d x = ∫ 0 1.052 x x 2 + 1 2 - x 5 + x d x Applying integration separately, = ∫ 0 1.052 x x 2 + 1 2 d x - ∫ 0 1.052 x 5 d x + ∫ 0 1

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ISBN: 9781285740621

Author: James Stewart

Publisher: Cengage Learning

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Chapter 5.1, Problem 38E

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Approximate x-coordinates of the points of intersection of the given curves, and find the area of the region bounded by the curves.

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Chapter 5.1, Problem 37E

Chapter 5.1, Problem 39E

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Approximate x -coordinates of the points of intersection of the given curves, and find the area of the region bounded by the curves.

Solution Summary: The author calculates the area of the region bounded by the curves.

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To find:

Approximate x-coordinates of the points of intersection of the given curves, and find the area of the region bounded by the curves.

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Chapter 5 Solutions

Approximate x -coordinates of the points of intersection of the given curves, and find the area of the region bounded by the curves.

Solution Summary: The author calculates the area of the region bounded by the curves.

Concept explainers

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To find: Approximate x-coordinates of the points of intersection of the given curves, and find the area of the region bounded by the curves.

Want to see the full answer?

Chapter 5 Solutions

To find:

Approximate x-coordinates of the points of intersection of the given curves, and find the area of the region bounded by the curves.