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Unformatted text preview: Math 21B
Kouba
Challenge Sheet 7 1.) SET UP BUT DO NOT EVALUATE integral(s) which represent the area of the region
bounded by the graphs of y : 3:1:2 — 2:4 and y = $3 + $2. 2.) SET UP BUT DO NOT EVALUATE integral(s) which represent the area of the region
bounded by the graphs of a.) yze‘m,y=$+1,and:r:2
i.) using vertical cross—sections.
ii.) using horizontal cross—sections. b.) y:3:c andyzx2—2m
i.) using vertical cross—sections.
ii.) using horizontal cross—sections. c.) y = sinus and y = 0 on the interval [0, 7r]
i.) using vertical cross—sections.
ii.) using horizontal crosssections. 3.) The base of a solid is in the wyplane bounded by the graphs of y = m2 and y = 233.
SET UP BUT DO NOT EVALUATE integral(s) which represent the volume of the solid
if cross—sections taken perpendicular to the w—axis are a.) squares. b.) triangles of height 5. c.) isosceles right triangles with one edge in the my—plane.
d.) semicircles with diameters in the myplane. e.) isosceles right triangles with hypotenuse in the nay—plane. 4.) Using the DISC METHOD, SET UP BUT DO NOT EVALUATE integral(s) which
represent the volume of the solid formed by revolving the region R, bounded by the given
graphs, about the designated line. a.) R: 3126731320, andyz?)
i.) about the m—axis
ii.) about the y—axis
iii.) about the line y = 5
iv.) about the line :1: = —2 b.) R: y=ﬁ,y:0,andm=4
i.) about the m—axis
ii.) about the yaxis
iii.) about the line y z —1
iv.) about the line a: : 100 C.) R: 31:33:. 22x,and:c=3
1.) about the xaxis
' ii.) about the yaxis
iii.) about the line 3/ = 6
iv.) about the line m = 1 5.) Repeat exercise 4.) using the SHELL METHOD. 6.) The region bounded by the graphs of y = 0, a: : 0, and y z 1 ~ :1: is revolved about
the line y =2 1 —— :3. Use any method to compute the volume of this solid. 5 7.) The region bounded by the graphs of y = m2 and y = :n is revolved. about the line
y = :3. Use any method to compute the volume of this solid. )V ...
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 Winter '09
 Kouba
 Calculus

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