Calculus 2 -- Test #2 -- SAMPLE Nrune_ _ _ _ _ _ _ _ _ _ _ _ _ ___ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the volume of the described solid. 1) The solid lies between planes perpendicular to the x-axis at x = -3 and x = 3. The cross sections perpendicular to the x-axis between these planes are squares whose bases run from the semicircle y=x2 to the semicircle y = ~.}9 A) 144 B) 36 ,,jg - 1) ____ - x2. D) 18 C) 72 2) The solid lies between planes perpendicular to the x-axis at x = - 6 and x = 6. The cross sections 2) _ __ perpendicular to the x-axis are semicircles whose diameters run from y =- ,.J36- x2 to y ="'36- x2. A) 72n B) 288n D) 576n C) 144n Find the length of the curve. 3) y = (4- x2/3) 312 from x = 1 to x = 8 A) 12 B) 6 3) _ __ D) 9 C) 18 4) x = ~(y- 1) 3/2 from y = 4 toy= 9 3 A) 19 B) 57 2 4) _ __ D)~ C) 38 3 3 E) 2 Set up an integral for the length of the curve. 5) X = yl/7, 0 S y S 5) _ __ 2 2 A)J ~ 49yl2/7 .~dy 0 C) I 0 2 .------ ,_4~9y'-1_217_+_1 dy 49yl2/7 B) I 2 .~dy 0 ~ 49yl2/7 2 .--~D) ,_7.,._y_61_7=+_1 dy 0 7y6!7 I Solve the problem. 6) Find the work done in winding up a 150-ft cable that weighs 4.00 lb/ft. A) 11,300 ftlb B) 135,000 ftlb C) 45,000 ftlb 6) _ __ D) 1200 ftlb 7) A vertical right circular cylindrical tank measures 22 ft high and 8 ft in diameter. It is full of oil weighing 60 lb/fP. How much work does it take to pump the oil to the level of the top of the tank? Give your answer to the nearest ft lb. B) 1,459,710 ft lb C) 12,164 ft lb D) 729,855 ft lb A) 2,919,419 ft lb 7) _ __ Evaluate the integral. 8) I -3x cos 4x dx 8) - - B) - 16 C) - 9) I ! 4 cos 4x - 3x sin 4x + C cos-1 x dx A)xcos-1x- p _l_ cos 4x _lx sin 4x + C D) - A) - _l_ cos 4x _1_ sin 4x + C _l_ cos 4x _lx sin 3x + C 16 4 16 4 9) - - B) x cos-1x +C +~1- x2 + C 1- x2 D) x cos-1x- ~1- x2 + C C) x cos-1x- 2-h- x2 + C 10) I 10) - - - x3ln 4x dx ! A) 1.. x4 In 4x - _!_ x4 + C B) In 4x - C) 1._ x4 In 4x - _!_ x5 + C 4 20 D) 1.. x4 In 4x + _!_ x4 + C 4 11) I 16 4 16 11) - - - 8 cos3 2x dx A) 4 sin 2x + ! sin3 2x + C B) 4 sin 2x - C) 8 sin 2x - 12) x4 + C ~ sin3 2x + C D) 4 sin 2x - I ! ! sin3 2x + C cos3 2x + C 12) _ _ tanS 3x dx l 12 1 6 1 3 I I A) - 1 tan4 3x + 1 tan2 3x- 1 1n 1 cos x I + C 3 6 12 B) -tan4 3x- -tan2 3x- -In cos x + C 1 4 1 2 1 C)utan 3x - tan 3x + ln I cosx 1 c + D) 6 13) I 3 ! tan4 3x - ~ tan2 3x - In I cos x I + C 13) - - - 7 sec4 x dx A)~ B) 7 tan x + tan3 x + C ~ tan3 x + C D) - ?_ tan3 x + C 3 C) 7(sec x + tan x)S+ C 2 ....-------,--~-~- - - - - - - ~-------~--------n--- Integrate the function. 14) J~9+x2 6 dx A)6Inl 14) - - - ~I+ c 2 B)-- + C 2 +9 X C)x+t\\ + D)6ln~!_+?l C 15) J~ + 36 - x2 dx A) C) 15) - - - !Ssin-1[~)+ ~ +C X 3~36- x2 C B) +~+C 36x ~36-x2 D)18x- x 3 +~ + C 2 ~ +C 2