Explanation Proof: The left sum defined for n rectangles on [ a , b ] is ∑ k = 1 n f ( x k − 1 ) Δ x . Where, Δ x = b − a n , x k = a + k Δ x . The right sum defined for n rectangles on [ a , b ] is ∑ k = 1 n f ( x k ) Δ x . Where, Δ x = b − a n , x k = a + k Δ x

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Chapter 4.2, Problem 53P

To determine

To prove: that if a function f is positive and concave up on [a,b] , then the trapezoid sum with n trapezoids is an always an over-approximation for the actual area.

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Chapter 4.2, Problem 52P

Chapter 4.2, Problem 1TF

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Chapter 4 Solutions

Calculus

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To prove: that if a function f is positive and concave up on [ a , b ] , then the trapezoid sum with n trapezoids is an always an over-approximation for the actual area.

Solution Summary: The author proves that if a function f is positive and concave up, the trapezoids are always an over-approximation for the actual area.

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To prove: that if a function f is positive and concave up on [a,b] , then the trapezoid sum with n trapezoids is an always an over-approximation for the actual area.

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Chapter 4 Solutions