Explanation Given Information: The provided functions are y = cos x and y = 2 − cos x for x = 0 to x = 2 π . Formula used: The formula of definite integral of ∫ a b cos u d u . ∫ a b cos u d u = [ sin u ] a b Here, n is the any positive integer. The formula of definite integral of ∫ a b d u . ∫ a b d u = [ u ] a b Graph: For the region bounded by graph of y = cos x and y = 2 − cos x for x = 0 to x = 2 π . Consider the provided function. y = cos x At x = 0 , y x = 0 = cos 0 = 1 At x = π 2 , y x = π 2 = cos π 2 = 0 At x = π , y x = π = cos π = − 1 At x = 3 π 2 , y x = 3 π 2 = cos 3 π 2 = 0 At x = 2 π , y x = 2 π = cos 2 π = 1 Now, the table for ordered pair ( x , y ) for the function y = cos x is shown below, x y 0 1 π / 2 0 π − 1 3 π / 2 0 2 π 1 Now also, consider the provided function. y = 2 − cos x At x = 0 , y x = 0 = 2 − cos 0 = 2 − 1 = 1 At x = π 2 , y x = π 2 = 2 − cos π 2 = 2 − 0 = 2 At x = π , y x = π = 2 − cos π = 2 − ( − 1 ) = 3 At x = 3 π 2 , y x = 3 π 2 = 2 − cos 3 π 2

10th Edition

ISBN: 8220101426222

Author: Larson

Publisher: CENGAGE L

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 8.5, Problem 53E

To determine

To graph: The region bounded by the functions, y=cosx and y=2−cosx for x=0 to x=2π and also calculate the area of the region.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.5, Problem 52E

Chapter 8.5, Problem 54E

Students have asked these similar questions

3.1 Limits 1. If lim f(x)=-6 and lim f(x)=5, then lim f(x). Explain your choice. x+3° x+3* x+3 (a) Is 5 (c) Does not exist (b) is 6 (d) is infinite

1 pts Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is Question 1 -0.246 0.072 -0.934 0.478 -0.914 -0.855 0.710 0.262 .

2. Answer the following questions. (A) [50%] Given the vector field F(x, y, z) = (x²y, e", yz²), verify the differential identity Vx (VF) V(V •F) - V²F (B) [50%] Remark. You are confined to use the differential identities. Let u and v be scalar fields, and F be a vector field given by F = (Vu) x (Vv) (i) Show that F is solenoidal (or incompressible). (ii) Show that G = (uvv – vVu) is a vector potential for F.

Chapter 8 Solutions

EBK CALCULUS: AN APPLIED APPROACH

Ch. 8.1 - For each angle, find a coterminal angle such that...Ch. 8.1 - Prob. 2CP Ch. 8.1 - Prob. 3CP Ch. 8.1 - Prob. 4CP Ch. 8.1 - Prob. 1SWU Ch. 8.1 - Prob. 2SWU Ch. 8.1 - Prob. 3SWU Ch. 8.1 - Prob. 4SWU Ch. 8.1 - Prob. 5SWU Ch. 8.1 - Prob. 6SWU

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.

To graph: The region bounded by the functions, y = cos x and y = 2 − cos x for x = 0 to x = 2 π and also calculate the area of the region.

Solution Summary: The author calculates the area of the region bounded by the functions y=mathrmcosx.

Concept explainers

Videos

To graph: The region bounded by the functions, y=cosx and y=2−cosx for x=0 to x=2π and also calculate the area of the region.

Want to see the full answer?

Chapter 8 Solutions