MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 --review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the area of the shaded region. ) f() = + - ) 0 0 (, 8) 0 (0, 0) (-, -) - -0 g() = A) 97 B) 78 C) 8 D) ) = + - = - ) A) 8 B) C) 9 D) 9

2 ) ) - = - - A) 7 = - B) C) 7 D) Find the area enclosed b the given curves. ) = -, = - A) 7 B) C) D) ) ) =, = A) B) C) D) ) Find the volume of the solid generated b revolving the region bounded b the given lines and curves about the -ais. ) =, = 0, = 0, = 9 ) A) π 7) = +, = 0, = -, = A) π B) π 7) 8) = sin, = 0, 0 π 8) A) π C) 8π D) π 9) = - + 0, =, = 0 A) 0π C) 0π D) 0π 9) 0) =, =, = 0 A) π 0)

3 ) = +, = + A) π B) 7π 07 C) π D) π ) Find the volume of the solid generated b revolving the region about the -ais. ) The region enclosed b =, = 0, = -, = A) 08 8 π ) ) The region enclosed b =, = 0, =, = ) A) π C) π D) π 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 = A) π C) 8 π D) π ) Use the shell method to find the volume of the solid generated b revolving the shaded region about the indicated ais. ) About the -ais ) = / A) 0π

4 ) About the -ais ) = = = - A) 0 π 7) About the -ais 7) = = - /9 A) 7 8π C) π D) π 8) About the -ais 8) =sin().8 A) π C) π D) 9π

5 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. 9) = 7, = 7, for 0 9) A) 8 7 π 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. 0) = -, = 0 0) A) 8 π Use the shell method to find the volume of the solid generated b revolving the region bounded b the given curves about the given lines. ) =, = ; revolve about the -ais ) A) π ) = -, =, = ; revolve about the line = A) 8 π ) Solve the problem. ) A bead is formed from a sphere of radius b drilling through a diameter of the sphere with a drill bit of radius. Find the volume of the bead. A) 8 0 π C) π D) π ) Find the length of the curve. ) = + from = to = ) A) B) 79 C) 7 D) ) = 8 + from = to = ) A) B) 7 C) 8 9 D) 9 9

6 Set up an integral for the length of the curve. ) = -, - ) A) C) / + 8 d -/ B) / - + d ( - ) -/ D) / -/ / -/ ( - ) - ( - ) d d 7) = sin, - π 0 A) 0 + cos d B) -π C) 0 + cos d D) -π 0 -π 0 -π + cos d + sin d 7) Solve the problem. 8) The gravitational force (in lb) of attraction between two objects is given b F = k/, where is the distance between the objects. If the objects are ft apart, find the work required to separate them until the are 0 ft apart. Epress the result in terms of k. A) k B) 0 k C) 0 k D) 9 0 k 8) 9) A vertical right circular clindrical tank measures 0 ft high and 8 ft in diameter. It is full of oil weighing 0 lb/ft. How much work does it take to pump the oil to the level of the top of the tank? Give our answer to the nearest ft lb. A) 0,0 ft lb B),0,7 ft lb C) 0,8 ft lb D),,7 ft lb 0) A swimming pool has a rectangular base 0 ft long and 0 ft wide. The sides are ft high, and the pool is full of water. How much work will it take to lower the water level feet b pumping the water out over the top of the pool? Assume that the water weighs. lb/ft. Give our answer to the nearest ft lb. A) 99,80 ft lb B),90 ft lb C),80 ft lb D) 99,80 ft lb ) The spring of a spring balance is.0 in. long when there is no weight on the balance, and it is 7. in. long with.0 lb hung from the balance. How much work is done in stretching it from.0 in. to a length of 0. in.? A) 99 lb in. B) 7 lb in. C).8 lb in. D).0 lb in. 9) 0) ) ) A force of 00 lb compresses a spring from its natural length of 9 in. to a length of in. How much work is done in compressing it from in. to 7 in.? A) 0.9 lb in. B) 9900 lb in. C) 00 lb in. D) 0,000 lb in. ) Find the center of mass of a thin plate of constant densit covering the given region. ) The region bounded b = and = A) = 0, = 8 B) = 0, = C) = 0, = 7 D) = 0, = 9 )

7 ) The region enclosed b the parabolas = and = A) = 0, = 8 B) =, = 0 C) = 0, = D) = 0, = ) Find the centroid of the thin plate bounded b the graphs of the given functions. Use δ = and M = area of the region covered b the plate. ) g() = and f() = + ) A) =, = 8 B) =, = C) =, = 8 D) =, = 8 Solve the problem. ) One end of a pool is a vertical wall ft wide. What is the force eerted on this wall b the water if it is 7 ft deep? The densit of water is. lb/ft. A) 00 lb B) 0,700 lb C),00 lb D),800 lb 7) A right triangular plate of base 8 m and height m is submerged verticall, as shown below. Find the force on one side of the plate if the top verte is m below the surface. (w = 9800 N/m) ) 7) m m 8 m A) 80,000 N B) 0,000 N C) 0,000 N D) 0,000 N 7

8 Answer Ke Testname: REVIEW ) A ) D ) C ) C ) B ) C 7) B 8) A 9) C 0) D ) C ) B ) A ) D ) B ) B 7) C 8) C 9) A 0) C ) D ) A ) B ) A ) D ) B 7) A 8) D 9) C 0) B ) B ) B ) D ) D ) C ) C 7) A 8

MAC 2311 Chapter 5 Review Materials Topics Include Areas Between Curves, Volumes (disks, washers, and shells), Work, and Average Value of a Function

MAC 2311 Chapter 5 Review Materials Topics Include Areas Between Curves, Volumes (disks, washers, and shells), Work, and Average Value of a Function MAC Chapter Review Materials Topics Include Areas Between Curves, Volumes (disks, washers, and shells), Work, and Average Value of a Function MULTIPLE CHOICE. Choose the one alternative that best completes