W11_MATH1020_CALCULUS2_TEST1_vB_Blue

W11_MATH1020_CALCULUS2_TEST1_vB_Blue - Calculus 11 Term...

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Unformatted text preview: Calculus 11 Term Test 1 W 2011 2 1. (3 marks each; total 9 marks) (b) fazcos2x (ix: J; X Mix ~ Sim/ulex = i-xmnlx +-1\_T(901X+C TAKE w: x ) 6&5}: (901% one», u: final» (0) Set up (do not evaluate) an integral calculating the force exerted on one side of the thin plate shown in the figure below: 1E was A MEASOLED $20M THE 4 ‘3 finance DOUJJO.‘ 4 _ . Fm~j gag-emw m ‘ 6 FkoM, sCmLArL A‘s: L = P =3 x: {,3 ~‘- 6-H q 1 3.. Calculus 11 Term Test 1 W 2011 1 2 2 2. (8 marks) Evaluate / 33—” da: 2 0 (w — 2X33? + 1) A9356 : 1‘1;_ t A + B41: wmfi AJAC. (Y-LMx‘HB X'L 114“ so 1%» = A C¥‘+l3+<15x+c1(x“7-) FOL 79:1,: \Q: 4:0 ‘3 A‘tl, FOL x=o -. 0 = 2+C~230 => C=4 mt m1 -. 3: Q+<E~E\)(~\) => f$==O \ \ le-k—x j S __ Ax = .2; .J__ o (1—1358ch 1x-L 1' X‘M Abe O 0 ll (1 aux—u + WAY O -:. lQA~\+QMtM\-SL|QA~1~W0 T t ~19“; \l Calculus 11 Term Test 1 W 2011 3. (8 marks) Evaluate the following improper integral: m , b [0 tan2x dx = 'Qv‘w S Qa/wlx 01V Calculus 11 Term Test 1 W 2011 5 3 4. (8 marks) Consider the definite integral / dm (do NOT evaluate it.) _1x+2 (a) Approximate the value of the integral, using the trapezoidal rule with 4 subintervals. (b) Find the maximum error in your approximation above. K(b — a)3 ,, (HINT: recall lET| g T, where If g K for a g m S b). n @ SS \ 0U B TR = 9:— (flCxoh Z'QUA-‘slgbcg+L§(¥Q+g(¥q)) X—‘cl “‘ .1. ..|_> = Jil‘l—fl—‘Z’WJJH at + s = \O\ 60 . f ’ _\ "C = ’L 6’) PM“ K” film: Q13, ’ 110‘) _ (my ’ lg x) QA—‘LY’ I/ Z _ . ' ~ 3 BECKEASmb r’ Lx‘135 Fol X U3 E \J :1 , 7" Fopcn'ou TAu'ue \Ts MAX'GQ x=-\. so Tmel‘éczs 3—43 ~ 15*“ i‘ =0“ Calculus 11 Term rTest 1 W’ 2011 6 5. (9 marks total) Answer the following questions in the space provided (a) (2 marks) Set up (do NOT evaluate) an integral for the volume of the solid obtained by rotating the curve 3; = 1'2 about the x-axis: for —1 g m g 1. \ ij‘ckx Answer: _\ (b) (2 marks) Set up (do NOT evaluate) an integral for the surface area of the solid obtained by rotating the area between 3) = cos 2m and the posi- tive LB—axis for 0 g :L' g 77/4. 1174 S N mix ‘8 \+ Hm'ullx Ab: Answer: 0 (c) (2 marks) To solve / tan3$sec3$ 011' by u-substitution, the best choice ofuis Answer: W X (d) (1 mark) True/False / seca: da: is an imprOper integral. 0 M012:— MOT DE‘éINED Answer; TRUE 2 e 1 mark The tri sub used for solvin / — 011' is: () ( ) g g $2M Answer: x: 1M9 0L X: Lose 3 (f) (1 mark) Evaluate/$+x dx —= X x"+x J~x 1.2 "6A.\¥\ + fix.L +C Answer: Calculus 11 Term Test 1 W 2011 7 6. (8 marks) (This question will take several steps; you should attempt it after you have completed the other questions on the test.) Evaluate / arctanfi dm (HINT: you may want to start with a substitution) TAKE w=€§,&w‘J—°{* ’30 A‘:2w&d d») _ 1— : v-90 we!» H1 2 Q‘— _ 1 u).— alto _ (AW L 1' ...
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