Sheet7 - Math 21B Kouba Challenge Sheet 7 1 SET UP BUT DO...

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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 cross-sections. 3.) The base of a solid is in the wy-plane 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.) semi-circles with diameters in the my-plane. 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 y-axis iii.) about the line y z —1 iv.) about the line a: : 100 C.) R: 31:33:. 22x,and:c=3 1.) about the x-axis ' ii.) about the y-axis 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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