Explanation Definition used: Let f be defined on a closed interval [ a , b ] , which is divided into n sub-intervals of equal length and x k * is any point in the k th subinterval [ x k − 1 , x k ] for k = 1 , 2 , ⋯ , n , then the Riemann sum on [ a , b ] can be written as ∑ k = 1 n f ( x k ) Δ x . It is known that Δ x is always positive

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter 5.2, Problem 4E

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To explain: Why the definite integral ∫abf(x) is negative if f(x)<0 on the interval [a,b] explain by using Riemann sums.

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Chapter 5.2, Problem 3E

Chapter 5.2, Problem 5E

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Chapter 5 Solutions

Calculus: Early Transcendentals (2nd Edition)

Ch. 5.1 - Suppose an object moves along a line at 15 m/s,...Ch. 5.1 - Given the graph of the positive velocity of an...Ch. 5.1 - Prob. 3E Ch. 5.1 - Explain how Riemann sum approximations to the area...Ch. 5.1 - Suppose the interval [1, 3] is partitioned into n...Ch. 5.1 - Prob. 6E Ch. 5.1 - Does a right Riemann sum underestimate or...Ch. 5.1 - Does a left Riemann sum underestimate or...Ch. 5.1 - Approximating displacement The velocity in ft/s of...Ch. 5.1 - Approximating displacement The velocity in ft/s of...

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Why the definite integral ∫ a b f ( x ) is negative if f ( x ) < 0 on the interval [ a , b ] explain by using Riemann sums.

Solution Summary: The author explains that if f(x)0 is negative, then the Riemann sum can be written.

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To explain: Why the definite integral ∫abf(x) is negative if f(x)<0 on the interval [a,b] explain by using Riemann sums.

Want to see the full answer?

Chapter 5 Solutions

Why the definite integral ∫ a b f ( x ) is negative if f ( x ) &lt; 0 on the interval [ a , b ] explain by using Riemann sums.

Solution Summary: The author explains that if f(x)0 is negative, then the Riemann sum can be written.

Concept explainers

Videos

To explain: Why the definite integral ∫abf(x) is negative if f(x)<0 on the interval [a,b] explain by using Riemann sums.

Want to see the full answer?

Chapter 5 Solutions

Why the definite integral ∫ a b f ( x ) is negative if f ( x ) < 0 on the interval [ a , b ] explain by using Riemann sums.