Explanation Given information: Given, h ( x ) = 1 2 x + 5 ; Δ x = 2 , x 0 = 2 . Riemann sum is ∑ i = 0 4 h ( x i ) Δ x . Calculation: Given, h ( x ) = 1 2 x + 5 ; Δ x = 2 , x 0 = 2 . Now, ∑ i = 0 4 h ( x i ) Δ x = h ( x 0 ) Δ x + h ( x 1 ) Δ x + h ( x 2 ) Δ x + h ( x 3 ) Δ x + h ( x 4 ) Δ x Since, x i + 1 = x i + To determine (b) The given Riemann sums. To determine (c) The given Riemann sums.

6th Edition

ISBN: 9781119267874

Author: Hughes-Hallett

Publisher: WILEY

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

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Question

Chapter 5.2, Problem 43P

To determine

(a)

The given Riemann sums.

To determine

(b)

The given Riemann sums.

To determine

(c)

The given Riemann sums.

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Chapter 5.2, Problem 42P

Chapter 5.3, Problem 1P

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(a) The given Riemann sums.

Solution Summary: The author calculates the given Riemann sums: h(x) = 12x+5.

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(a) The given Riemann sums.

(b) The given Riemann sums.

(c) The given Riemann sums.

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Chapter 5 Solutions

(a)

The given Riemann sums.

(b)

The given Riemann sums.

(c)

The given Riemann sums.