Explanation Given: The equations are x = ( y − 1 ) 2 , x − y = 1 ; about x = − 1 . Calculation: Show the equations as below: x = ( y − 1 ) 2 (1) x − y = 1 (2) Plot a graph for the equations x = ( y − 1 ) 2 and x = y 2 + 1 using the calculation as follows: Calculate y value using Equation (1) Substitute 0 for x in Equation (1). 0 = ( y − 1 ) 2 0 = y − 1 y = 1 Hence, the co-ordinate of ( x , y ) is ( 0 , 1 ) . Calculate y value using Equation (1) Substitute 1 for x in Equation (1). 1 = ( y − 1 ) 2 1 = y − 1 ± 1 = y − 1 y = 1 ± 1 y 1 = 0 y 2 = 2 Hence, the co-ordinate of ( x , y ) is ( 1 , 0 ) and ( 1 , 2 ) . Calculate y value using Equation (2). Substitute 0 for x in Equation (2). 0 − y = 1 y = − 1 The co-ordinate of ( x , y ) is ( 0 , − 1 ) . Calculate y value using Equation (2). Substitute 1 for x in Equation (2). 1 − y = 1 y = 1 − 1 = 0 The co-ordinate of ( x , y ) is ( 1 , 0 ) . Similarly calculate the coordinate values up to bound the region in the graph. Draw the washer as shown in Figure 1. Calculate the volume using the method of washer: V = ∫ a b π { [ f ( y ) ] 2 − [ g ( y ) ] 2 } d y (3) Calculate the y value: Substitute ( y − 1 ) 2 for x in Equation (2). ( y − 1 ) 2 − y = 1 y 2 − 2 y + 1 − y − 1 = 0 y 2 − 3 y = 0 y ( y − 3 ) = 0 (4) Solve Equation (4). y 1 = 0 y 2 = 3 Consider g ( y ) = − x + ( y − 1 ) 2 (5) Substitute ( − 1 ) for x in Equation (5). g ( y ) = − ( − 1 ) + ( y − 1 ) 2 = ( y − 1 ) 2 + 1 = y 2 − 2 y + 1 + 1 = y 2 − 2 y + 2 Consider f ( y ) = − x + y + 1 (6) Substitute ( − 1 ) for x in Equation (6)

Single Variable Calculus: Early Transcendentals

8th Edition

ISBN: 9781305270336

Author: James Stewart

Publisher: Cengage Learning

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 6.3, Problem 43E

To determine

To find: The volume of the resulting solid by the region bounded by given curve using the method of washer.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.3, Problem 42E

Chapter 6.3, Problem 44E

Students have asked these similar questions

i need help please

(#1) Consider the solid bounded below by z = x² and above by z = 4-y². If we were to project this solid down onto the xy-plane, you should be able to use algebra to determine the 2D region R in the xy-plane for the purposes of integration. Which ONE of these limite of integration would correctly describe R? (a) y: x24x: -22 - (b) y: 22 x: 04-y² (c) y: -√√4-x2. →√√4x²x: −2 → 2 (d) z: 24-y² y: -2 → 2 (e) None of the above

X MindTap - Cenxxxx Answered: tat "X A 26308049 X 10 EKU-- SP 25: X E DNA Sequenc X b/ui/evo/index.html?elSBN=9780357038406&id=339416021&snapshotid=877369& GE MINDTAP , Limits, and the Derivative 40. Answer 5 4-5 t-10 5 f(x) = 2x - 4 if x ≤0 if x 0 10 ++ -4-3-2-1 f(x) = MacBook Pro Search or type URL 5 1234 x² +1 if x = 0 if x = 0 +

Chapter 6 Solutions

Single Variable Calculus: Early Transcendentals

Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Prob. 7E Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

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.

The volume of the resulting solid by the region bounded by given curve using the method of washer.

Solution Summary: The author calculates the volume of the resulting solid by the region bounded by given curve using the method of washer.

Concept explainers

Videos

To find: The volume of the resulting solid by the region bounded by given curve using the method of washer.

Want to see the full answer?

Chapter 6 Solutions