Using the method of cylindrical shells, set up but do not evaluate an integral for the volume of the solid generated when the region R inthe first quadrant bounded by the graphs of y = V4 - x, y = 0, and x = 0 is revolved about (a) the line x = 2 and (b) the liney = -2.(a)2m(2 – x)V4 – x² áxV =V =1(2 – x)V4 – x² dx27(2 – x)(4 – x) áxV =V =2x(2 + x)V4 – ? åx(b)V =2л(2 + у) /4 — у? dуя(2 + у)у|4 – y² ayV =V =27(2 – y)(4 – y) ảy42я(2 + у) у4 — у dyV =

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Answered: Using the method of cylindrical shells,…

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...

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Using the method of cylindrical shells, set up but do not evaluate an integral for the volume of the solid generated when the region R in the first quadrant bounded by the graphs of y=16−x2⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√, y=0,y=16-x2, y=0, and x=0x=0 is revolved about (a) the line x=4x=4 and (b) the line y= −4.y⁢= -4.(a) V=∫402π(4+x)16−x2⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√ⅆxV⁢=∫042π(4+x)16-x2ⅆx V=∫402π(4−x)(16−x2)ⅆxV=∫042π(4-x)(16-x2)ⅆx V=∫402π(4−x)16−x2⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√ⅆxV=∫042π(4-x)16-x2ⅆx V=∫160π(4−x)16−x2⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√ⅆxV=∫016π(4-x)16-x2ⅆx (b) V=∫160π(4+y)16−y2⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√ⅆyV=∫016π(4+y)16-y2ⅆy V=∫402π(4+y)16−y2⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√ⅆyV=∫042π(4+y)16-y2ⅆy V=∫402π(4−y)(16−y2)ⅆyV=∫042π(4-y)(16-y2)ⅆy V=∫1602π(4+y)16−y2⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√ⅆy
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the curves x= 4y2-y3 and x=0 about the x axis. Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the curves y=x2 , y=0, x=1 and x=2 about the line x=1.
A solid of revolution is formed by rotating about the x-axis the area bounded betweenx = ,0 x = 1 and the curve given by the table x 0 0.25 0.5 0.75 1.0f(x) 1.0 0.9896 0.9587 0.9089 0.8415 Find the volume of the solid so formed using i) Trapezodial rule ii) Simpson’s rule
Consider the region bounded by the curve y = 4x2 - x3 , the x-axis, and the lines x = 1 and x = 3. The region is rotated about the y-axis. Use shell method to find the volume of the solid of revolution. Express your answer in exact form.
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
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).
Apply the cylindrical shell method to obtain the volume of the solid generated when the region bounded by the curve y^2 = x^3, x=2 and the x-axis is revolved about the x-axis. (SHOW THE SOLUTION)
volume of the solid generated when the region bounded by y = 9 − x2 and y = 2x + 6 is revolved about the x-axis.
Using the shell method set up an integral to find the volume of a solid of revolution rotating it about the line y=1 for a region bounded by y=x^5, y=1 , x=0 in the first quadrant using shells.
Set up a triple integral for the volume of the solid. Do not evaluate the integral. The solid bounded above by the cylinder z = 4 − x2 and below by the paraboloid z = x2 + 3y2
use a triple integral to find the volume of the solid bounded by the graphs of the equations. use a triple integral to find the volume of the solid bounded by the graphs of the equations. z = xy, z = 0, 0 ≤ x ≤ 3, 0 ≤ y ≤ 4
Consider the solid formed by revolving the region bounded by y = √x, y = 0, x = 1, and x = 3 about the x-axis. Find the value of x in the interval [1, 3] that divides the solid into two parts of equal volume.

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