Consider the region bounded by the curves 6 and x = 1. Vr²+36 y = 7², y 2 If this region is revolved around the x - axis, the volume of the resulting solid can be computed in (at least) two different ways using integrals. (Sketching the graph of the situation might help you answer the following.) where a = = (a) First of all it can be computed as a single integral [² = h(x) dx and = h(x) This method is commonly called the method of

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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Author:Bruce Crauder, Benny Evans, Alan Noell
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ChapterA: Appendix
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Consider the region bounded by the curves
6
and x = 1.
Vr²+36
y = 7², y
-2
If this region is revolved around the x - axis, the volume
of the resulting solid can be computed in (at least) two
different ways using integrals. (Sketching the graph of
the situation might help you answer the following.)
where a =
=
(a) First of all it can be computed as a single integral
S.
=
h(x) dx
and
=
h(x)
This method is commonly called the method of
(Enter 'DW' for Disks/Washers or 'CS' for Cylindrical
Shells).
Transcribed Image Text:Consider the region bounded by the curves 6 and x = 1. Vr²+36 y = 7², y -2 If this region is revolved around the x - axis, the volume of the resulting solid can be computed in (at least) two different ways using integrals. (Sketching the graph of the situation might help you answer the following.) where a = = (a) First of all it can be computed as a single integral S. = h(x) dx and = h(x) This method is commonly called the method of (Enter 'DW' for Disks/Washers or 'CS' for Cylindrical Shells).
(b) Alternatively, this volume can be computed as a sum
of integrals
where a =
and
f(y) =
g(y) =
mb
[* f (y) dy +
a
, C =
g(y) dy
,b=
This method is commonly called the method of
(Enter 'DW' for Disks/Washers or 'CS' for Cylindrical
Shells).
(c) Either way, we find that the volume of the solid of
revolution is
cubic units.
Transcribed Image Text:(b) Alternatively, this volume can be computed as a sum of integrals where a = and f(y) = g(y) = mb [* f (y) dy + a , C = g(y) dy ,b= This method is commonly called the method of (Enter 'DW' for Disks/Washers or 'CS' for Cylindrical Shells). (c) Either way, we find that the volume of the solid of revolution is cubic units.
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