(a) Explanation Given information: Consider the function f ( x ) = x 2 − 3 x − 4 ; [ − 5 , 5 ] . 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 = 10 Δ x = b − a n = 5 + 5 10 = 10 10 = 1 x k = a + k Δ x = − 5 + k ( 1 ) = k − 5 ⇒ x k − 1 = k − 6 The left sum is given by = ∑ k = 1 n f (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: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Question

Chapter 4.6, Problem 23S

(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 22C

Chapter 4.6, Problem 24S

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Chapter 4 Solutions

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The signed area with at least eight rectangles.

Solution Summary: The author analyzes the function f(x)=x2-3x-4; n is a positive integer.