(a) Explanation Given information: Consider the function f ( x ) = sin x ; [ 0 , π ] ; n = 3 Formula used: Let f is continuous function defined on an interval [ a , b ] , n is a positive integer. Δ x = b − a n , x k = a + k Δ x . The trapezoid sum of n- rectangles is = ∑ k = 1 n f ( x k − 1 ) + f ( x k ) 2 Δ x Calculation: From the given data, we have Δ x = b − a n = π − 0 3 </ (b) To determine To find: The upper sum of the given function f on [ a , b ] .

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 4.2, Problem 28S

(a)

To determine

To find: The trapezoid sum of the given function f on [a,b].

(b)

To determine

To find: The upper sum of the given function f on [a,b].

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Chapter 4.2, Problem 27S

Chapter 4.2, Problem 29S

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The trapezoid sum of the given function f on [ a , b ] .

Solution Summary: The author explains the trapezoid sum of the given function f on [a,b].

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To find: The trapezoid sum of the given function f on [a,b].

To find: The upper sum of the given function f on [a,b].

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