Explanation Formula used: “If f is continuous function on the interval [ a , b ] , then the area under the graph of a function and coordinate axis is Area = ∫ a b f ( x ) d x .” Definition used: Improper integral: “If f is continuous on [ a , ∞ ) , then ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x . If it exists and finite, then it converges otherwise diverges.” Theorem used: Fundamental Theorem: “Let f be a continuous function on [ a , b ] . If F is anti-derivative of f on [ a , b ] , then ∫ a b f ( x ) d x = F ( b ) − F ( a ) .” Calculation: The given function is f ( x ) = 3 e − x on the interval [ 0 , ∞ ) . Here, the area is defined by, Area = ∫ 0 ∞ 3 e − x d x . Find the limit of the improper integral ∫ 0 ∞ 3 e − x d x to check whether it is convergent or divergent

10th Edition

ISBN: 8220102020252

Author: RITCHEY

Publisher: PEARSON

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Chapter 16, Problem 49RE

To determine

To find: The area under the graph of a function f(x)=3e−x over the interval [0,∞) , if it is possible.

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Chapter 16, Problem 48RE

Chapter 16, Problem 50RE

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Chapter 16 Solutions

EBK FINITE MATHEMATICS AND CALCULUS WIT

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Knowledge Booster

The area under the graph of a function f ( x ) = 3 e − x over the interval [ 0 , ∞ ) , if it is possible.

Solution Summary: The author explains that the area under the graph of a function f(x)=3e-x is 3

To find: The area under the graph of a function f(x)=3e−x over the interval [0,∞) , if it is possible.

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Chapter 16 Solutions