11th Edition

ISBN: 9780135189405

Author: Michael Sullivan

Publisher: PEARSON

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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 14.5, Problem 24AYU

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

a. What area does the integral represent?

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

b. Provide a graph that illustrates this area.

To determine

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

c. Use a graphing utility to approximate this area.

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Chapter 14.5, Problem 23AYU

Chapter 14.5, Problem 25AYU

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Chapter 14 Solutions

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Ch. 14.1 - Graph f( x )={ 3x2ifx2 3ifx=2 (pp.100-102)Ch. 14.1 - Prob. 2AYU Ch. 14.1 - Prob. 3AYU Ch. 14.1 - Prob. 4AYU Ch. 14.1 - True or False lim xc f( x )=N may be described by...Ch. 14.1 - Prob. 6AYU Ch. 14.1 - lim x2 ( 4 x 3 )Ch. 14.1 - lim x3 ( 2 x 2 +1 )Ch. 14.1 - lim x0 x+1 x 2 +1 Ch. 14.1 - Prob. 10AYU

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The following for an integral ∫ 1 3 ( − 2 x + 7 ) d x . a. What area does the integral represent?

Solution Summary: The author explains how the integral represents an area under the graph of 2 x + 7 from 1 to 3. Provide a graph that illustrates this area.

Concept explainers

Videos

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

a. What area does the integral represent?

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

b. Provide a graph that illustrates this area.

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

c. Use a graphing utility to approximate this area.

Want to see the full answer?

Chapter 14 Solutions

Additional Math Textbook Solutions

The following for an integral ∫ 1 3 ( − 2 x + 7 ) d x . a. What area does the integral represent?

Solution Summary: The author explains how the integral represents an area under the graph of 2 x + 7 from 1 to 3. Provide a graph that illustrates this area.

Concept explainers

Videos

To find: The following for an integral ∫ 1 3 ( −2x + 7 )dx . a. What area does the integral represent?

To find: The following for an integral ∫ 1 3 ( −2x + 7 )dx . b. Provide a graph that illustrates this area.

To find: The following for an integral ∫ 1 3 ( −2x + 7 )dx . c. Use a graphing utility to approximate this area.

Want to see the full answer?

Chapter 14 Solutions

Additional Math Textbook Solutions

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

a. What area does the integral represent?

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

b. Provide a graph that illustrates this area.

To find: The following for an integral $\int_{1}^{3} (- 2 x + 7) d x$ .

c. Use a graphing utility to approximate this area.