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Find the volume of the solid generated by revolving the region bounded by 2y = e-x², the x-axis and the y-axis about the y-axis using disk method.

Find the volume of the solid generated by revolving the region bounded by 2y = e-x², the x-axis and the y-axis about the y-axis using disk method.

Elementary Geometry For College Students, 7e
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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Convergent or divergent. (Show the graph and strip)

Area = =ff(x) dx (Vertical Strip); where a or b is +/-infinity. (Then apply the improper integral *limits*) Area = f(x) dy (Horizontal Strip); where cord is +/- infinity. (Then apply the improper integral *limits*) Volume: (Then apply the improper integral *limits*) (Circular Disk): Horizontal Axis of Rev V = R(x) dx Vertical Axis of Rev.: V=IR(y) Pºdy (Circular ring/Washer): Horizontal Axis of Rev Vertical Axis of Rev.: V=Rx)-[xPJdx V=R²¹-¹)dy. (Cylindrical Shell): Infinite Limits (Convergent or Divergent) A.= f(x) dx = lim f(x) dx B.= f(x) dx = limf(x) dx cf(x) dx=ff(x) dx + f(x) dx Discontinuous Integral (Convergent or Divergent) 1. @x=ac x=a: (discontinuity) f(x) dx=lim ff(x) dx 2. @x=b: (discontinuity) f(x) dx=lim f(x) dx 3. @x=C; a<c<b (discontinuity) fox dx=f(x) dx + f(x) dx V=20 vidr -00 <c< 00
Transcribed Image Text:Area = =ff(x) dx (Vertical Strip); where a or b is +/-infinity. (Then apply the improper integral *limits*) Area = f(x) dy (Horizontal Strip); where cord is +/- infinity. (Then apply the improper integral *limits*) Volume: (Then apply the improper integral *limits*) (Circular Disk): Horizontal Axis of Rev V = R(x) dx Vertical Axis of Rev.: V=IR(y) Pºdy (Circular ring/Washer): Horizontal Axis of Rev Vertical Axis of Rev.: V=Rx)-[xPJdx V=R²¹-¹)dy. (Cylindrical Shell): Infinite Limits (Convergent or Divergent) A.= f(x) dx = lim f(x) dx B.= f(x) dx = limf(x) dx cf(x) dx=ff(x) dx + f(x) dx Discontinuous Integral (Convergent or Divergent) 1. @x=ac x=a: (discontinuity) f(x) dx=lim ff(x) dx 2. @x=b: (discontinuity) f(x) dx=lim f(x) dx 3. @x=C; a<c<b (discontinuity) fox dx=f(x) dx + f(x) dx V=20 vidr -00 <c< 00
Find the volume of the solid generated by revolving the region bounded by 2y = e-x², the x-axis and the y-axis about the y-axis using disk method.
Transcribed Image Text:Find the volume of the solid generated by revolving the region bounded by 2y = e-x², the x-axis and the y-axis about the y-axis using disk method.
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