Name Find the area the shaded region.
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1 Berkele Cit College Due: HW - Chapter 6 - Applications of Integration Name Find the area of the shaded region. 1) = = ) ) 6 = - 1 ) 4 = Instructor: K Pernell 1
2 ) ) 1 = = sin(!) Calculate the area of the region bounded b the graphs of the given equations. 4) =, = 9 4) ) =, = ) 6) = 0, = 1, = + 6, = + 6) 7) = ( - ) 4, = ( - ) 7) Find the volume of the solid generated b revolving the region R bounded b the graphs of the given equations about the -ais. 8) =, = 0, between = 1 and = 8)
3 Find the volume of the solid generated b revolving the region R bounded b the graphs of the given equations about the -ais. 9) =, =, = 0 9) 10) = 4, = 0, between = 1 and = 6 10) Find the volume of the solid generated b revolving the region R bounded b the graphs of the given equations about the -ais. 11) = , = 6, = 0 11) 1) = csc, =, between =! 4 and =! 4 1) Find the volume of the solid generated b revolving the region R bounded b the graphs of the given equations about the -ais. 1) bounded b =, b the line =, and b the -ais 1) Find the volume of the solid generated b revolving the region about the given line. 14) The region in the first quadrant bounded b the line + = 10, b the -ais, and b the -ais, about the line = -. 14) 1) The region in the first quadrant bounded b the line =, b -ais, and b the line = 1, about the line = )
4 16) The region in the first quadrant bounded b the line =, b the curve =, and b the -ais, about the line =. 16) Use the shell method to find the volume of the solid generated b revolving the region bounded b the given curves and lines about the -ais. 17) = 4, = 0, = 4 17) 18) = 9, = 9 18) 19) = 8 -, =, = 0 19) Find the volume of the solid generated b revolving the region bounded b the given curves about the -ais. 0) =, = -, = 1 0) 1) =, = -, = 1) ) = 7, = 14, = 7 ) Find the volume of the solid generated b revolving the region about the given line. ) The region bounded above b the line =, below b the curve = -, and on the right b the line =, about the line = ) 4
5 4) The region in the first quadrant bounded above b the line =, below b the curve =, and on the left b the -ais, about the line = -1 4) Solve the problem. ) The spring of a spring balance is 6.0 in. long when there is no weight on the balance, and it is 8. in. long with 9.0 lb hung from the balance. How much work is done in stretching it from 6.0 in. to a length of 1.7 in.? ) 6) A force of 100 lb compresses a spring from its natural length of 0 in. to a length of 1 in. How much work is done in compressing it from 1 in. to 8 in.? 6) Find the average value over the given interval. 7) f() = 11 ; [1, e] 7) 8) f() = - + ; [0, 8] 8) 9) f() = 10 sin ; [0,!] 9) 0) f() = sec tan ; [0,! ] 0)
6 Answer Ke Testname: HW_CH6 1) 97 1 Objective: (6.1) Find Area of Shaded Region ) 9 Objective: (6.1) Find Area of Shaded Region ) 4 Objective: (6.1) Find Area of Shaded Region 4) 81 ) Objective: (6.1) Find Area Bounded b Curves I 1 1 Objective: (6.1) Find Area Bounded b Curves I 6) 4 Objective: (6.1) Find Area Bounded b Curves II 7) 7 Objective: (6.1) Find Area Bounded b Curves III 8) 14 Objective: (6.) Find Volume: Revolution About -Ais (Disk Sections) 9) 4! Objective: (6.) Find Volume: Revolution About -Ais (Disk Sections) 10) 40 Objective: (6.) Find Volume: Revolution About -Ais (Disk Sections) 11) 7! Objective: (6.) Find Volume: Revolution About -Ais (Washer Sections) 1) 4! - 8! Objective: (6.) Find Volume: Revolution About -Ais (Washer Sections) 1) 486! Objective: (6.) Find Volume: Revolution About -Ais (Washer Sections) 14) 160 Objective: (6.) Find Volume: Revolution About Line (Disk/Washer Sections) 1) 9 14! Objective: (6.) Find Volume: Revolution About Line (Disk/Washer Sections) 6
7 Answer Ke Testname: HW_CH6 16) 9! Objective: (6.) Find Volume: Revolution About Line (Disk/Washer Sections) 17) 1! Objective: (6.) Find Volume: Revolution about -Ais 18) 7 10! Objective: (6.) Find Volume: Revolution about -Ais 19) 16! Objective: (6.) Find Volume: Revolution about -Ais 0) Objective: (6.) Find Volume: Revolution about -Ais 1) 1! Objective: (6.) Find Volume: Revolution about -Ais ) 49 Objective: (6.) Find Volume: Revolution about -Ais ) 6! Objective: (6.) Find Volume: Revolution about Line 4) 7! Objective: (6.) Find Volume: Revolution about Line ) 110 in.-lb Objective: (6.) Solve Apps: Springs 6) 600 in.-lb Objective: (6.) Solve Apps: Springs 7) 11 e - 1 8) 19 9) 0! Objective: (.) Find Average Value of Function Objective: (.) Find Average Value of Function Objective: (.) Find Average Value of Function 0) Objective: (.) Find Average Value of Function 7
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