(a) Explanation Given information: Consider the function f ( x ) = cos x ; [ − 2 π , 2 π ] . 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 left sum of n- rectangles is = ∑ k = 1 n f ( x k − 1 ) Δ x Calculation: From the given data, we have [ a , b ] = [ − 5 , 5 ] Let n = 8 Δ x = b − a n = 2 π + 2 π 8 = π 2 x k = a + k Δ x = − 2 π + k ( π 2 ) ⇒ x k − 1 (b) To determine To find: The absolute area between the graph of f and the x- axis from x = a to x = b .

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Question

Chapter 4.6, Problem 24S

(a)

To determine

To find:The signed area with at least eight rectangles.

(b)

To determine

To find: The absolute area between the graph of f and the x- axis from x=a to x=b .

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Chapter 4.6, Problem 23S

Chapter 4.6, Problem 25S

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The signed area with at least eight rectangles.

Solution Summary: The author explains how to find the signed area with at least eight rectangles.