3. Use the shell method to set up hut DO NOT EVALUATE the integral for finding the volume of revolution of the same solid bounded by y = 0, x= 5, and the curve y =(x-2)',when it is revolved about the x-axis by completing these steps: a. Use a different color pen to highlight the boundary lines and only the boundary lines. b. Lightly shade the region to be revolved. c. Indicate the axis of rotation with a curved arrow around it. d. Draw a sample rectangle (strip) in the region to be revolved. e. Label the differential. f. Label the radius and the height of the shell. g. Identify the limits of integration by drawing the first strip and the last strip. h. The integral is:

3. Use the shell method to set up hut DO NOT EVALUATE the integral for finding the volume of revolution of the same solid bounded by y = 0, x= 5, and the curve y =(x-2)',when it is revolved about the x-axis by completing these steps: a. Use a different color pen to highlight the boundary lines and only the boundary lines. b. Lightly shade the region to be revolved. c. Indicate the axis of rotation with a curved arrow around it. d. Draw a sample rectangle (strip) in the region to be revolved. e. Label the differential. f. Label the radius and the height of the shell. g. Identify the limits of integration by drawing the first strip and the last strip. h. The integral is:

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Optimization

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 selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

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 that have length, breadth, and height (or depth).

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.

Question

**Transcription for Educational Website**

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**Problem 3: Setting Up an Integral Using the Shell Method**

Use the shell method to set up (but **DO NOT EVALUATE**) the integral for finding the volume of revolution of the solid bounded by $ y = 0 $, $ x = 5 $, and the curve $ y = (x - 2)^2 $ when it is revolved about the x-axis by following these steps:

a. Use a different color pen to highlight the boundary lines and only the boundary lines.

b. Lightly shade the region to be revolved.

c. Indicate the axis of rotation with a curved arrow around it.

d. Draw a sample rectangle (strip) in the region to be revolved.

e. Label the differential.

f. Label the radius and the height of the shell.

g. Identify the limits of integration by drawing the first strip and the last strip.

h. The integral is:

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**Graph Explanation:**

The graph provided is a parabolic curve representing the function $ y = (x-2)^2 $. It is plotted from $ x = 0 $ to $ x = 5 $. The parabola opens upwards, with its vertex at the point $ (2, 0) $. The vertical axis is labeled with intervals that allow the curve to be easily visualized, extending beyond the limit of interest $ x=5 $. The region of interest for setting up the integral is bounded by the x-axis ($ y=0 $) and the vertical line $ x=5 $.

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Expert Solution

Step 1

Given the solid bounded by the points $y = 0, x = 5$ and the curve $y = {(x - 2)}^{2}$ is revolved about the x-axis.

(a)

Step 2

(b)

(c)

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