Explanation Given information: Graph of y = ( 14 x + 18 ) − 4 / 5 for x ≥ 1 . Formula used: ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x = L , where f ( x ) is a nonnegative function for x ≥ a and a be the fixed number. Proof: First, write the improper integral using the given information and formula. By using formula, The area defined by an improper integral is ∫ 1 ∞ ( 14 x + 18 ) − 4 / 5 d x as shown in the figure below: Let b > 1 , then lim b → ∞ [ ∫ 1 b ( 14 x + 18 ) − 4 / 5 d x ] . Now solve improper integral by using the substitution method as follows: 14 x + 18 = u ⇒ 14 d x = d u ⇒ d x = 1 14 d u When x = 1 , u = 32 ; when x = b , u = 14 b + 18

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Chapter 9.6, Problem 19E

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To prove: The region under the graph of y=(14x+18)−4/5 for x≥1 cannot be assigned any finite number as its area shown in the figure:

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Chapter 9.6, Problem 18E

Chapter 9.6, Problem 20E

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To prove: The region under the graph of y = ( 14 x + 18 ) − 4 / 5 for x ≥ 1 cannot be assigned any finite number as its area shown in the figure:

Solution Summary: The author explains how the region under the graph of y=(14x+18)-4/5 cannot be assigned any finite number.

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To prove: The region under the graph of y=(14x+18)−4/5 for x≥1 cannot be assigned any finite number as its area shown in the figure:

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Chapter 9 Solutions