Explanation Given information: The region bounded by the parabola x = 2 and x = − 2 . Calculation: Provide the Equation of curve as shown below. y = x 2 (1) Sketch the region bounded by the x axis and the curve y = x 2 shown in Figure 1. Refer to Figure 1. Consider a vertical strip has center of mass ( x ˜ , y ˜ ) = ( x , x 2 2 ) The length of the strip is x 2 and the width of strip is dx . Calculate area of the strip as shown below. d A = length × width Substitute x 2 for length and dx for width. d A = x 2 d x Calculate the mass of the strip as shown below. d m = δ d A Substitute x 2 d x for d A . d m = δ x 2 d x Calculate the mass of the plate as shown below. M = ∫ d m = δ ∫ − 2 2 x 2 d x = δ [ x 3 3 ] − 2 2 = δ 3 ( 2 3 − ( − 2 ) 3 ) = δ 3 ( 8 + 8 ) = 16 δ 3 Calculate the moment of the strip about x axis as shown below. y ˜ d m = δ 2 x 2 ( x 2 ) d x = δ 2 x 4 d x Calculate the moment of the plate about x axis as shown below

Pearson eText University Calculus: Early Transcendentals -- Instant Access (Pearson+)

4th Edition

ISBN: 9780136880912

Author: Joel Hass, Christopher Heil

Publisher: PEARSON+

See similar textbooks

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 se…

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, integratio…

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.

Videos

Question

Chapter 6, Problem 40PE

To determine

Calculate the center of mass of a thin plate.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6, Problem 39PE

Chapter 6, Problem 41PE

Students have asked these similar questions

1) let X: N R be a sequence and let Y: N+R be the squence obtained from x by di scarding the first meN terms of x in other words Y(n) = x(m+h) then X converges to L If and only is y converges to L- 11) let Xn = cos(n) where nyo prove D2-1 that lim xn = 0 by def. h→00 ii) prove that for any irrational numbers ther exsist asquence of rational numbers (xn) converg to S.

4.2 Product and Quotient Rules 1. 9(x)=125+1 y14+2 Use the product and/or quotient rule to find the derivative of each function. a. g(x)= b. y (2x-3)(x-1) c. y== 3x-4 √x

4.2 Product and Quotient Rules 1. Use the product and/or quotient rule to find the derivative of each function. 2.5 a. g(x)=+1 y14+2 √x-1) b. y=(2x-3)(x-:

Chapter 6 Solutions

Pearson eText University Calculus: Early Transcendentals -- Instant Access (Pearson+)

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.