Explanation Given: The function is: f ( x ) = 1 − e − 3 x Formula used: The total area is: A = ∫ x 1 x 2 f ( x ) d x Calculation: To find the total area, compute the area above the x − a x i s and under the x − a x i s separately. Now, find the x − i n t e r c e p t s of the graph: 1 − e − 3 x = 0 e − 3 x = 1 e − 3 x = e 0 − 3 x = 0 So, x = 0 The graph of the f ( x ) is: The graph crosses the x − a x i s at ( 0 , 0 ) . Here, it is provided to concern with the graph between -1 and 2 . So, 0 is the relevant x-intercept . Then, the area below the x-axis is: ∫ − 1 0 ( 1 − e − 3 x ) d x = ( x − e − 3 x − 3 ) − 1 0 = ( 0 − e − 3 × 0 − 3 ) − ( ( − 1 ) − e − 3 × − 1 − 3 ) = − [ ( 1 3 ) − ( − 1 + e 3 3 ) ] = − 4 3 + e 3 3 So, the area of the lower region is ( − 4 3 + e 3 3 )

Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)

12th Edition

ISBN: 9780134767628

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Question

Chapter 13.5, Problem 42E

To determine

To calculate: The area between the x-axis and f(x) over the interval [−1,2].

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Chapter 13.5, Problem 41E

Chapter 13.5, Problem 43E

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Chapter 13 Solutions

Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)

Ch. 13.1 - Checkpoint 1 Find an antiderivative for each of...Ch. 13.1 - Checkpoint 2 Find each of the...Ch. 13.1 - Prob. 3CP Ch. 13.1 - Prob. 4CP Ch. 13.1 - Prob. 5CP Ch. 13.1 - Prob. 6CP Ch. 13.1 - Prob. 7CP Ch. 13.1 - Checkpoint 8 The marginal cost at a level of...Ch. 13.1 - 1. What must be true of F(x) and G(x) if both are...Ch. 13.1 - 2. How is the antiderivative of a function related...

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The area between the x-axis and f ( x ) over the interval [ − 1 , 2 ] .

To calculate: The area between the x-axis and f(x) over the interval [−1,2].

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Chapter 13 Solutions