math 5a exam 7.pdf - Exam 7 Chapter 5,Math 5A Spring 2020 a Name ~)\u00b0Ir,1 f Mr Andreasyan rv\u00be.J Instructions Show all work Partial credit will not be

math 5a exam 7.pdf - Exam 7 Chapter 5,Math 5A Spring 2020 a...

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Mr . Andreasyan Instructions. Exam 7, Chapter 5,Math 5A Spring 2020 a_. , \;\ '\ rv ¾ Nam e ~" )°Ir, 1 f\ .J Show all work. Partial credit will not be given, if only answer is indicated. Box your final answer. GOOD LUCK . 1. Find the area of the region bounded by the curves y = x 2 and y = x Ave°'-=)~ ~-t1-r).X -._ '£__ - '(~ II 1- . "1 o c_ -\----"'~--1r--;;1 X C \_ - \ ) - Co -o }-:c \-f) ~ L -:.- L~TS ~'- - t ~ - 1 -- 0 5 C - 's) ( ~\) 6~ ----1-sr----f---7..-<----t--;; X 1 \() -= 3 - \ ::_ S_, ( '-- - [ 1 '1:1)) cl~ -:_ l - v/ -~~\s (0- °l- l\ )- (~ " hs) -\3§J -\
4. Use the disk method to find the volwne of the solid obtained by rotating the region bounded by the given curves about the given axis. y = I - x 2 ; y = O; about the x-~is. , \I . RC XJ \ - 'X 1- t+-7 \J:: nj~ C\-'fl-"/- rN, . ":_\\ S \ (l-11 1 +~Vi') otx , L =-TI Gt - ,._ '{i, t L )\ 1 :- \\ 6'- if) :: ~!] "S O ',,- <; 5. Use the washer method to find the vo wne of the solid obtained by rotating the region bounded by the given curves about the given axis \2- -= 12._ - 'X t \j-=- nSt [({~~~)uty(\) J <Ax {' -_ L-\ ~ -\ -- 1 x~ \ \ 1-n ':: T\ s O C l - X 1 ) <AX -:. id)- 3) I 0 X l I ' 6. Use the washer method to find the volume of the solid obtained by rotating ~~B bounde by the given curves about the given axis \ \ t _ Svt .;px = JY.. x = aboutx = -2 \J -:_ \\ Jo ,,,,1 _ '( 1.. ,\I - b . . / - '\Is; C~-r~)t..-(~-rl."/ct~ X c_ 11 S> lj 1.. - S '.'.) +4F \1 \ c~ tf) C + c) ~C':i '- 1,_ ,~ 1 ~ -\ lt~1)'1-'f - 4 '-J ,A--n(~- 1 { ~; l ~-1:1) ~-n) -i Wt~ 'J- ¾ -4 - -~ '\ \} "s · 1; o - ---s---; -~
7. Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the given axis. 2 = x; x = 2y; about the y-axis AC~)~ n(lj/1-~\\(~£)'--\(l ?.::: -i> I ('-f )l.)'-e. ?~ L__~!::..-------~~xA C Vf) -=-L\ \\ \1}-_ A cv;J =-'ti CL\ j '--~J \\-: ( l-\ U?-"'-~1.0-:: \\ C ~'13-~]2.. t\ o t. ;J j bu '---S o 11 ~C1) - ~ 1 y X ) '\\ 11\ S" \I :- ( -= \2 n 8. Use the method of cylindrical she s o m t e volume of the solid obtained by rotating the region bounded by the given curves about the given line. Y = x3 x > y = about x = 2 Ol 9. Use the method of cylindrical shells to fmd the volume of the solid obtained by rotating the region bounded by the given curves about the given axis. ' - ' ' - XL\ x = 2y2; x = y2 + 1; abouty 'L'tl \r -:='2 'v\e_ l1\\.,=-(\b-i.k\) -( 2v-/) -~'1+\ \J-= j_: Cl\\~) (-11)"1-TI) t::. ---+---I-----) X :: 2\\ J ° C-•~{t ':) ·--) := 11\ c~\ -t ¾) [_ -;'j = - 2 \\ . d.._ J c,{ ~- L

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