16BSolutionsII

# 16BSolutionsII - SHORT CALCULUS MAT 16B Section 001 Fall...

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Unformatted text preview: SHORT CALCULUS MAT 16B, Section 001 * Fall 2011 Midterm 2 DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO NAME: ...................................................... .. ID NUMBER: ...................................................... .. SIGNATURE: ...................................................... .. Keep you student’s i.d. Visible in front of you. No books, no calculators or electronic devices allowed. Turn your cell phone off. No communication among the students will be tolerated. SHOW ALL YOUR WORK Problem Total Points Student’s Score Total 37 (+3) PROBLEM 1. [15pts] Compute the following antiderivatives: / 2 3+\/a': = ubmﬁnwamm dag: L 3 Li‘j-A‘éhk z QSWEM = Hu~IL(u(ul+C ulme £e¥ m 34D? ' Thu—3 ' ‘53: J (=) «ix—.UML ' I dx er =Z(u~3)olu /2-(2w) (2)d — Quota ~ Jo.” Q ~ iS‘UQW-LC 81H 3/ COS .7} .T— \- L + - L ‘ where MAJ-C} (A: QULY 3;: lCoSlX /(4x—1)1n(3x)dm= 131+)! U; (1“ U\ :LDV" (2‘: 3‘; V: 73(5) BQthy/Myolx: (55> )& 5>< - RAP—gtng :Ux‘~>(>(M3>X\ ﬁzwa :(mﬁwn X”+>< +Ac: PROBLEM 1. (CONTINUED) /cot(\$)d;r= Sg—EJV‘ SEPdl/ °' : (“(SEIAXI4C when m Keir (A: Eu‘oor ' CL“: cwx I /\$25f3:?4dx= (Demo/160.3%»! ¥L+ 33(41 1 OHWU“) > r . , 5>+5 ‘ A i ‘ Am) +L~A+Ln< (T76 Ml Krakow X‘+g}_q ~ >Hq + X“ ~ (34000?!) HQ‘AM/ i :0 96: (D =9 3:2 ( 3‘44 74 : 5-15 5 3 5 >r-H) 3: __£ XXL-LS5qu : 53Gb! 4* Jr 33H y ZQIHH) + ZLuIBr—r) + C PROBLEM 2. [16pts] Compute the following deﬁnite integrals: 1 _1/1 I l J/ /e:z;2 (ix: (“4" & §~YCIX 0 340* a X” - A v i» K L .. l S5; (A- )l ' . x» g 4&9 EV" u (A ‘l/x 3—14»: SQCJL eC-+C‘~e >( I \ ‘4 r/ y l ‘ I ‘ 31,4 (HM g :3le Z “a, E. ~Q a é»o“ ‘9 )( A~o+ {. ‘I/A . i. 33 “44 e. 1 (Lu 6"; A—~o" wke’r 10 /:r\3/:1:—2dx= We Eel (A: >#~L ' 2 X: 2 cl (4‘0 4/ ‘yl lguwwl 3.9 3.‘1.i>. :%Z4ZZ~4lDS-LZL( > (I PROBLEM 2. (CONTINUED) 5 1 0° 1 ~/ /1 V5 by“) \ Moo 1/ Ema 14¢ ‘ uzx U' U‘:{ V= 1/ {,1 q —- % igl’obmhr 0 Vi Cole (041 = %-Z(‘ PROBLEM 3. [6pts] i.[3pts] Set up but do not compute the integral(s) to find the area of the region between the two curves = 2x3 — 3:162 + :L' and 9(33) 2 —J:2 + 5x, sketched below. lu’ccrrechbu (club: 53’ 96+ )r = - X L1. 3‘} (=1 2X3 — [X L- ‘br t 0 (=1 X LXL~>~Z) =0 r00 “=7 x Lx- 13m.) = 0 Heme : £45,3-. Botlxs—inqutiy 4 i: £~2XZ+ZX°+HY elk. —| gm) ii.[3pts] Find the volume of the solid obtained by revolving around the x—axis the surface delimited on the left by :1: = 0, on the right x = 2, above by the function f = V e295 — x3 + 1 and below by y = 0. L Wm“ :WEO HOWE»: “If g: aux X’s-H ) clx ewéze, X +y>o -YiLle_q+L_L :: eq-§ L > 11 PROBLEM 4. [3pts, extra, credit] [3pts] Assume that is an odd function such that f(x)d:r = 2 and ff” f(:c)dx = 1. Compute 3F £20”)de 3 4M4" ‘ S7546)ch 13 ...
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16BSolutionsII - SHORT CALCULUS MAT 16B Section 001 Fall...

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