Explanation Given: ∫ 1 2 f ( x ) d x = 5 , ∫ − 2 1 f ( x ) d x = 8 Calculation: We know ∫ a b f ( x ) d x = ∫ a c f ( x ) d x + ∫ c b f ( x ) d x , where c is any number . Using the above property, we have ∫ − 2 2 f ( x ) d x = ∫ − 2 1 f ( x ) d x + ∫ 1 2 f ( x ) d x ∫ − 2 2 f ( x ) d x = 8 + 5 ∫ − 2 2 f ( x ) d x = 13 ∫ − 2 2 f ( x ) d x = 2 ∫ 0 2 f ( x ) d x = 13 (Since f is an even function, use the property of even functions that states ∫ − a a f ( x ) d x = 2 ∫ 0 a f ( x ) d x

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 5, Problem 82CRE

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To Evaluate:

$\int_{0}^{1} f (x) d x$ , assuming that f is an even continuous function such that $\int_{1}^{2} f (x) d x = 5$ , $\int_{- 2}^{1} f (x) d x = 8$

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Chapter 5, Problem 81CRE

Chapter 5, Problem 83CRE

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Chapter 5 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 5.1 - Prob. 1PQ Ch. 5.1 - Prob. 2PQ Ch. 5.1 - Prob. 3PQ Ch. 5.1 - Prob. 4PQ Ch. 5.1 - Prob. 5PQ Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E

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∫ 0 1 f ( x ) d x , assuming that f is an even continuous function such that ∫ 1 2 f ( x ) d x = 5 , ∫ − 2 1 f ( x ) d x = 8

Solution Summary: The author explains that if f is an even continuous function, use the property of even functions.

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To Evaluate:

$\int_{0}^{1} f (x) d x$ , assuming that f is an even continuous function such that $\int_{1}^{2} f (x) d x = 5$ , $\int_{- 2}^{1} f (x) d x = 8$

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Chapter 5 Solutions

∫ 0 1 f ( x ) d x , assuming that f is an even continuous function such that ∫ 1 2 f ( x ) d x = 5 , ∫ − 2 1 f ( x ) d x = 8

Solution Summary: The author explains that if f is an even continuous function, use the property of even functions.

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To Evaluate: ∫01f(x)dx, assuming that f is an even continuous function such that ∫12f(x)dx=5, ∫−21f(x)dx=8

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Chapter 5 Solutions

To Evaluate:

$\int_{0}^{1} f (x) d x$ , assuming that f is an even continuous function such that $\int_{1}^{2} f (x) d x = 5$ , $\int_{- 2}^{1} f (x) d x = 8$