Explanation Consider u = − x (1) Differentiate both sides of Equation (1). d u = − d x − d u = d x Calculate the lower limit value of u using Equation (1). Substitute a for x in Equation (1). u = − a Calculate the upper limit value of u using Equation (1). Substitute b for x in Equation (1). u = − b The integral function is, ∫ a b f ( − x ) d x (2) Apply lower and upper limits for u in Equation (2). Substitute u for ( − x ) and ( − d u ) for dx in Equation (2). ∫ a b f ( − x ) d x = ∫ − a − b f ( u ) ( − d u ) = − ∫ − a − b f ( u ) d u (3) Consider u = x (4) Differentiate both sides of Equation (4)

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ISBN: 9781305266636

Author: James Stewart

Publisher: Cengage Learning

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Chapter 4.5, Problem 61E

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To prove: The statement ∫abf(−x)dx=∫−b−af(x)dx and draw a diagram to interpret this equation geometrically for f(x)≥0 and 0<a<b.

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Chapter 4.5, Problem 60E

Chapter 4.5, Problem 62E

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To prove: The statement ∫ a b f ( − x ) d x = ∫ − b − a f ( x ) d x and draw a diagram to interpret this equation geometrically for f ( x ) ≥ 0 and 0 < a < b .

Solution Summary: The author explains how to draw a diagram to interpret the equation geometrically for f(x)ge 0and0

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To prove: The statement ∫abf(−x)dx=∫−b−af(x)dx and draw a diagram to interpret this equation geometrically for f(x)≥0 and 0<a<b.

Want to see the full answer?

Chapter 4 Solutions

To prove: The statement ∫ a b f ( − x ) d x = ∫ − b − a f ( x ) d x and draw a diagram to interpret this equation geometrically for f ( x ) ≥ 0 and 0 &lt; a &lt; b .

Solution Summary: The author explains how to draw a diagram to interpret the equation geometrically for f(x)ge 0and0

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To prove: The statement ∫abf(−x)dx=∫−b−af(x)dx and draw a diagram to interpret this equation geometrically for f(x)≥0 and 0<a<b.

Want to see the full answer?

Chapter 4 Solutions

To prove: The statement ∫ a b f ( − x ) d x = ∫ − b − a f ( x ) d x and draw a diagram to interpret this equation geometrically for f ( x ) ≥ 0 and 0 < a < b .