9th Edition

ISBN: 9781337613927

Author: Stewart

Publisher: CENGAGE L

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Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…

Integration

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Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

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Textbook Question

Chapter 8.2, Problem 3E

The given curve is rotated about the x -axis. Set up, but do not evaluate, an integral for the area of the resulting surface by integrating (a) with respect to x and (b) with respect to y .

3. x = ln ( 2 y + 1 ) , 0 ⩽ y ⩽ 1

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Chapter 8.2, Problem 2E

Chapter 8.2, Problem 4E

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Chapter 8 Solutions

Calculus, Early Transcendentals

Ch. 8.1 - Use the arc length formula (3) to find the length...Ch. 8.1 - Use the arc length formula to find the length of...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Find the exact length of the curve. 9....Ch. 8.1 - Find the exact length of the curve. 10....

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The given curve is rotated about the x -axis. Set up, but do not evaluate, an integral for the area of the resulting surface by integrating (a) with respect to x and (b) with respect to y . 3. x = ln ( 2 y + 1 ) , 0 ⩽ y ⩽ 1

Solution Summary: The author explains how to find the integral for the area of the resulting surface of a curve by integrating the curve with respect to x axis.

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Chapter 8 Solutions