Explanation Given information: f ( x ) = x 2 on [0,5] . 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 right Riemann sum is given by R R S = ∑ k = 1 n f ( x k ) Δ x Calculation: Find the right sum Δ x = b − a n = 5 − 0 n = 5 / n x k = a + k Δ x = 0 + k ( 5 / n ) = 5 k n ⇒ f ( x k ) = ( 5 k n ) 2 The right Riemann sum is given by R R S = ∑ k = 1 n ( 5 k n ) 2 5 n = ( 5 )

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Question

Chapter 4.5, Problem 4TB

To determine

To find: The exact area under the graph of f(x) with the use of limits of Riemann sums.

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Chapter 4.5, Problem 3TB

Chapter 4.5, Problem 0C

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Chapter 4 Solutions

Calculus

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ACP Ch. 4 - Prob. BCP Ch. 4 - Prob. CCP Ch. 4 - Prob. DCP

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The exact area under the graph of f ( x ) with the use of limits of Riemann sums.

Solution Summary: The author explains how to find the exact area under the graph of f(x) with the use of limits of Riemann sums.

To find: The exact area under the graph of f(x) with the use of limits of Riemann sums.

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Chapter 4 Solutions