Explanation Given information: The equation of the graph is y = ( x + 1 ) − 3 / 2 for x ≥ 3 Explanation: Definition: Let a be fixed and suppose that f ( x ) is a non-negative function for x ≥ a , and if lim b → ∞ ∫ a b f ( x ) d x = L , then ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x = L . First, write the improper integral using the given information and definition. By using the definition, The area defined by an improper integral is ∫ 3 ∞ ( x + 1 ) − 3 / 2 d x . Let b > 3 , then lim b → ∞ ∫ 3 b ( x + 1 ) − 3 / 2 d x . Now, solve the improper integral as follows: ∫ 3 b ( x + 1 ) − 3 / 2 d x = ( − ( x + 1 ) − 1 / 2 1 / 2 | 3 b ) Simplifying, = ( − 2 ( x + 1 ) − 1 / 2 | 3 b ) = − 2 ( b + 1 ) − 1 / 2 − ( − 2 ( 3 + 1 ) − 1 / 2 ) = − 2 ( b + 1 ) − 1 / 2 + 2 4 1 / 2 = − 2 ( b + 1 ) − 1

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Chapter 9.6, Problem 17E

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The area under the graph of y=(x+1)−3/2 for x≥ 3

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Chapter 9.6, Problem 16E

Chapter 9.6, Problem 18E

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Chapter 9 Solutions

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The area under the graph of y = ( x + 1 ) − 3 / 2 for x ≥ 3

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The area under the graph of y=(x+1)−3/2 for x≥ 3

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Chapter 9 Solutions