(a) Explanation Given information: Consider the definite integral ∫ − 3 2 x 2 d x . 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 right sum of n- rectangles is = ∑ k = 1 n f ( x k ) Δ x Calculation: From the given data, we have [ a , b ] = [ − 3 , 2 ] Δ x = b − a n = 2 − ( − 3 ) n = 5 n x k = a + k Δ x = − 3 + k ( 5 / n ) = − 3 + ( 5 k / n ) The right sum is given by = ∑ k = 1 n f ( x k ) Δ x = ∑ k = 1 n ( x k (b) To determine To find: The value of definite integral with the given values of n. (c) To determine To find: The exact value of the given definite integral as n tends to infinite.

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Question

Chapter 4.3, Problem 44S

(a)

To determine

To find: The formula for n- rectangle right sum of the given definite integral f on [a,b].

(b)

To determine

To find: The value of definite integral with the given values of n.

(c)

To determine

To find: The exact value of the given definite integral as n tends to infinite.

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Chapter 4.3, Problem 43S

Chapter 4.3, Problem 45S

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Chapter 4 Solutions

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The formula for n- rectangle right sum of the given definite integral f on [ a , b ] .

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To find: The formula for n- rectangle right sum of the given definite integral f on [a,b].

To find: The value of definite integral with the given values of n.

To find: The exact value of the given definite integral as n tends to infinite.

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Chapter 4 Solutions