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W11_MATH1020_CALCULUS2_TEST1_vC_Pink

# W11_MATH1020_CALCULUS2_TEST1_vC_Pink - Calculus II Term...

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Unformatted text preview: Calculus II Term Test 1 W 2011 2 1. (3 marks each; total 9 marks) (60/ﬂ dm— 83\$“— : lQM\u.\-\-C 332—3:B+2 _ (C) Set up (do not evaluate) an integral calculating the force exerted on one Fm siM'xwv A‘S: c-w H ‘1’ \$0 u):U<-\-)c :7—JD:\%’ Calculus II Term Test 1 2. (8 marks) Evaluate / II ’5’ (f 3 1w. so; TAKE X= S M9 Ax = S \$09419 x s \5 255—20“ So @oQ s Calculus II Term Test 1 W 2011 3. (8 marks) Evaluate the following improper integral: 0° 2—2 . _ - f1 ny/Zydyz a, 39% 5/”11/130‘13 Calculus II Term Test 1 W 2011 5 3 4. (8 marks) Consider the deﬁnite integral / e233 dm (do NOT evaluate it.) —1 (a) Approximate the value of the integral, using Simpson’s rule with 4 subin— tervals. (b) Find the maximum error in your approximation above. _ 5 (HINT: recall |E3| S %, where |f(4)(:c)| S K for a S a: g b). 3 @ X 81% A)“ 91” sq ‘5 Lia? (&Cx93+9 QUOA’Z Q69) All gbc 33+ &(¥q)) = i— (€‘1+R€Q+l€?—+R€H+€c) Calculus II Term Test 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; = ﬂ about the m—axis, for 1 S :12 S 2. 'l. j’ll—xokx. \ Answer: (b) (2 marks) Set up (do NOT evaluate) an integral for the surface area of the solid obtained by rotating the area between y = ﬂ and the positive m—axis for 1 S m g 3. 3 jmﬁii \+Q3x— 60.x \ (c) (2 marks) To solve / tan3msecgm dm by a—substitution, the best choice Answer: ofuis Answer: m X (d) (1 mark) True/False / seem dm is an improper integral. 0 32;, mT bends!) Kr 1;. Answer: TRUE (e) (1 mark) In the context of solving / \$2 cos (x + 1) dm by parts the best choice of u is: 1 Answer: a: X (f) (1 mark) Evaluate / cos2(2:r) +sin2(2:r) d3: 0 Calculus II 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.) ex Evaluate [m d3: '5 (HINT: you may want to start with a substitution) (TAKE u.= ef‘ , GET Au, = 9321» = dim uL—BUJ’L Asure ‘ - __\__ _ _A_ (S “Rama —QL—\Iu-Z) — “A + wz WANT A& so L = A (UL—2) +\$(UL-\) VQL U..=\: c—As) Ac—l “=1: It: [A = y— with“ UL—\ = — QMWM + Q» luau +C = _L~l€v-‘\+wc-z\+c (= Mg: \+C> ...
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W11_MATH1020_CALCULUS2_TEST1_vC_Pink - Calculus II Term...

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