y = sin(x), y = 0, x = 0, x = πExercise (a)the volume of the solid formed by revolving the region about the x-axisStep 1The region is bounded by the graphs of the equationsy = sin x, y = 0, x = 0, and x = .AxFor the representative rectangle, the radius of the solid of revolution isR(x) = sin xsin(x)According the disk method, the volume of solid of revolution, whe the area is revolve2✔= * [° [R(X)] ²V = TTherefore,Hence,V 11 = *.6² (sStep 2Use the half angle identity for sin² x.cos 2xsin²x =(sin(x))V = π1-*6* (²-y=sin(x)= [X-sin 2x= -0(π2cos 2x2R(x)dx.dx.Xdx) - (0)]42The volume of the solid of revolution is V =aboutaxis

Answered: Image /qna-images/answer/4c6a2fe4-5d59-4ab6-8d04-4e11bf0ef7e4.jpg

Answered: y = sin(x), y = 0, x = 0, x = Exercise…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Similar questions

A solid is generated by revolving the region bounded by y = (1/ 2) x2 and y = 2 about the y-axis. A hole, centered along the axis of revolution, is drilled through this solid so that one-fourth of the volume is removed. Find the diameter of the hole
A solid is generated by revolving the region bounded by y = √(9 − x2) and y = 0 about the y-axis. A hole, centered along the axis of revolution, is drilled through this solid so that one-third of the volume is removed. Find the diameter of the hole.
A solid is generated by revolving the region bounded by the following about the y-axis. y = 1/4x2 y = 4 A hole, centered along the axis of revolution, is drilled through this solid so that one-fourth of the volume is removed. Find the diameter of the hole. (Round your answer to three decimal places.)
The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method. x = 1 − y4 x = 0, about the line x = 4
The region between the curve y = 2/x and the x-axis from x = 1to x = 4 is revolved about the x-axis to generate a solid. Find the center of mass of a thin plate covering the region if the plate’s density at the point (x, y) is δ(x) = √x.
1. Find the volume generated by revolving about the line y = 0 the area under the arch of the sine curve y = sin x from x = 0 to x = π 2. Find the volume of the solid generated by revolving about y =1 the area bounded by the curve y = e^x , OX and the lines x = –1 and x = 0. 3. Find the volume of the solids of revolution generated when the region bounded by the curve y = x^2 , the x – axis and the lines x = 1 and x = 2 is revolved about the x – axis.
Find the volume of the solid generated by revolving the region bounded by the graphs of the equationsabout the line x = 4. Express the result as an exact value.y = 3 radical x; y = 0; x = 1; x = 4
Find the volume of the solid generated by revolving the region bounded by the graphs of the following equations about the indicated line. Draw a picture of the region to be rotated along with a representative rectangle. Clearly indicate the METHOD that you are using. Give a brief explanation of why you chose to use that particular method. Then, find the volume. y= x^2, y= 2x, about the line x= -2.
The region bounded by the given curve is rotated about the specified axis. Find the volume V of the resulting solid by any method. x2 + (y − 2)2 = 4; about the y-axis
1.Find the volume of the solid generated by revolving the region in the first quadrant bounded above by the curve y = x^2 , below by the x-axis, and on the right by the line x = 1, about the line x = -1 2.The region in the first quadrant enclosed by the parabola y = x^2 , the y-axis, and the line y = 1 is revolved about the line x = 3/2 to generate a solid. Find the volume of the solid Answer it correctly. Show complete solution.
Find the volume of the solid generated by revolving the region bounded by the graphs of the equationsabout the x-axis. Express the result as an exact value. y=9-x2 , y=x+3
A solid is generated by revolving about the x-axis the region bound-ed by the graph of the positive continuous function y = ƒ(x), the x-axis, the fixed line x = a, and the variable line x = b, b> a. Its volume, for all b, is b^2 - ab. Find ƒ(x).

SEE MORE QUESTIONS

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS