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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 = ixmnlx +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 _
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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.
(YLMx‘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$==O
\ \ lek—x j S __ Ax = .2; .J__ o (1—1358ch 1xL 1' X‘M Abe
O 0 ll (1 aux—u + WAY O :. lQA~\+QMtM\SLQA~1~W0 T
t ~19“; \l Calculus 11 Term Test 1 W 2011 3. (8 marks) Evaluate the following improper integral: m , b
[0 tan2x dx = 'Qv‘w S Qa/wlx 01V Calculus 11 Term Test 1 W 2011 5 3 4. (8 marks) Consider the deﬁnite integral / dm (do NOT evaluate it.) _1x+2 (a) Approximate the value of the integral, using the trapezoidal rule with 4
subintervals. (b) Find the maximum error in your approximation above. K(b — a)3 ,,
(HINT: recall lET g T, where If g K for a g m S b).
n @ SS \ 0U B TR = 9:— (ﬂCxoh Z'QUA‘slgbcg+L§(¥Q+g(¥q)) X—‘cl “‘ .1. .._>
= Jil‘l—ﬂ—‘Z’WJJH at + s
= \O\
60
. f ’ _\ "C = ’L
6’) PM“ K” ﬁlm: Q13, ’ 110‘) _ (my ’ lg x) QA—‘LY’
I/ Z _ .
' ~ 3 BECKEASmb r’ Lx‘135 Fol X U3 E \J :1 , 7" Fopcn'ou TAu'ue \Ts MAX'GQ x=\. so Tmel‘éczs 3—43 ~
15*“ i‘ =0“ Calculus 11 Term rTest 1 W’ 2011 6
5. (9 marks total) Answer the following questions in the space provided (a) (2 marks) Set up (do NOT evaluate) an integral for the volume of
the solid obtained by rotating the curve 3; = 1'2 about the xaxis: for
—1 g m g 1. \ ij‘ckx Answer: _\ (b) (2 marks) Set up (do NOT evaluate) an integral for the surface area of
the solid obtained by rotating the area between 3) = cos 2m and the posi
tive LB—axis for 0 g :L' g 77/4. 1174 S N mix ‘8 \+ Hm'ullx Ab: Answer: 0 (c) (2 marks) To solve / tan3$sec3$ 011' by usubstitution, 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—
: v90
we!» H1 2 Q‘—
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 Spring '11
 PaulaTu

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