Find the volume of the solid generated by revolving around the y- axis, the region bounded by 1 y = x = 2, x = 4, and the x-axis. (4-x)2/

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...
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equals to DIVERGENT. (Cylindrical shell method)

Find the volume of the solid generated by revolving around the y- axis, the region bounded by
1
y = (4x)²x = 2, x = 4, and the x-axis.
Transcribed Image Text:Find the volume of the solid generated by revolving around the y- axis, the region bounded by 1 y = (4x)²x = 2, x = 4, and the x-axis.
Infinite Limits (Convergent or Divergent)
A.=
f(x) dx = _lim_ f f(x) dx
too
B.=
f(x) dx =
f(x) dx
= lim ff(x) dx
t-00
c. f f(x) dx=ff(x) dx + + f(x) dx
Discontinuous Integral (Convergent or Divergent)
1. @x = a: (discontinuity)
f f(x) dx= lim f f(x) dx
t-a+
2. @x=b: (discontinuity)
f(x) dx= lim
f(x) dx
3. @x = C; a < c < b (discontinuity)
f(x) dx=ff(x) dx + f f (x) dx
-00 <c<∞0
Transcribed Image Text:Infinite Limits (Convergent or Divergent) A.= f(x) dx = _lim_ f f(x) dx too B.= f(x) dx = f(x) dx = lim ff(x) dx t-00 c. f f(x) dx=ff(x) dx + + f(x) dx Discontinuous Integral (Convergent or Divergent) 1. @x = a: (discontinuity) f f(x) dx= lim f f(x) dx t-a+ 2. @x=b: (discontinuity) f(x) dx= lim f(x) dx 3. @x = C; a < c < b (discontinuity) f(x) dx=ff(x) dx + f f (x) dx -00 <c<∞0
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