Explanation Given information: The integral ∫ − 1 1 ( x 2 − 1 ) d x is the negative of the area between the graph of f ( x ) = x 2 − 1 and x -axis for − 1 ≤ x ≤ 1 . Concept used: If the graph lies below the x-axis, then each value of f ( x ) is negative so each f ( x ) Δ x is negative and the area gets counted negative. The equation f ( x ) = x 2 − 1 represents a parabola which lies below that x-axis between x = − 1 and x = 1 . The area under the graph of f ( x ) = x 2 − 1 and x-axis for − 1 ≤ x ≤ 1 is shown in the following figure

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Question

Chapter 5, Problem 25SYU

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To indicate:

Whether the statement “The integral ∫−11(x2−1)dx is the negative of the area between the graph of f(x)=x2−1 and x -axis for −1≤x≤1 ” is true or false.

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Chapter 5, Problem 24SYU

Chapter 5, Problem 26SYU

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Chapter 5 Solutions

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Knowledge Booster

To indicate: Whether the statement “The integral ∫ − 1 1 ( x 2 − 1 ) d x is the negative of the area between the graph of f ( x ) = x 2 − 1 and x -axis for − 1 ≤ x ≤ 1 ” is true or false.

Solution Summary: The author explains that the integral displaystyle is the negative of the area between the graph and the x-axis.

To indicate:

Whether the statement “The integral ∫−11(x2−1)dx is the negative of the area between the graph of f(x)=x2−1 and x -axis for −1≤x≤1 ” is true or false.

Want to see the full answer?

Chapter 5 Solutions

To indicate: Whether the statement “The integral ∫ − 1 1 ( x 2 − 1 ) d x is the negative of the area between the graph of f ( x ) = x 2 − 1 and x -axis for − 1 ≤ x ≤ 1 ” is true or false.

Solution Summary: The author explains that the integral displaystyle is the negative of the area between the graph and the x-axis.

To indicate: Whether the statement “The integral ∫−11(x2−1)dx is the negative of the area between the graph of f(x)=x2−1 and x -axis for −1≤x≤1 ” is true or false.

Want to see the full answer?

Chapter 5 Solutions

To indicate:

Whether the statement “The integral ∫−11(x2−1)dx is the negative of the area between the graph of f(x)=x2−1 and x -axis for −1≤x≤1 ” is true or false.