Explanation Given: a , b , and c are real numbers. Concept Used: The definite integral ∫ a b f ( x ) d x represents the area between the graph of f ( x ) and x -axis on the interval [ a , b ] . The area that is bounded by the graph of f ( x ) above the x -axis is positive. The area that is bounded by the graph of f ( x ) below the x -axis is negative. Area of rectangle = Length × Width Calculation: In order to prove that the definite integral ∫ a b c d x = c ( b − a ) , first plot the graph of the function f ( x ) = c on the interval [ a , b ] . And then break the region bounded by the graph and x -axis using some geometric shapes like triangles, rectangles or circles and find their area. Use the concept that the definite integral ∫ a b f ( x ) d x represents the area between the graph of f ( x ) and x -axis on the interval [ a , b ]

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 4.3, Problem 58P

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To prove that ∫abc dx=c(b−a) for any real numbers a , b , and c , using geometry.

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Chapter 4.3, Problem 57P

Chapter 4.3, Problem 59P

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To prove that ∫ a b c d x = c ( b − a ) for any real numbers a , b , and c , using geometry.

Solution Summary: The author explains how to prove that the definite integral displaystyle 'int' is c(b-a) for any real numbers using geometry.

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To prove that ∫abc dx=c(b−a) for any real numbers a , b , and c , using geometry.

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