1505 2006 TEST 4 - YORK UNIVERSITY FACULTY OF ARTS...

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Unformatted text preview: YORK UNIVERSITY FACULTY OF ARTS DEPARTMENT OF MATHEMATICS AND STATISTICS MATH 1505 D 6.0, YEAR 2006-07 MATHEMATICS FOR THE LIFE AND SOCIAL SCIENCE Instructor : Dr Igor Poliakov TEST #4 MARCH 27, 2007 Name (print) (Family) (Given) Student ID. Instructions: 1. This is a closed-book T t. Calculators are permitted. 2. \ 4. YOU ARE ALLOWE TO USE AID SHEET. 5. USE PEN TW FINAL ANSWER. 6. DRAW A BOX AROUND YOUR FINAL ANSWERS. 7. DURATIO Test #4 contains 10 quesfio below: (Signature) ST IS ONE HOUR AND 30 MIN. 11 11 pages. Read the instructions carefully and sign Page 1 ofll 1. [10]. Use substitution to evaluate the indefmjte integral: I (x — 3)dl:(x — 3) r) y-‘3=‘Z (7') jig»?! (z) 2) £11773- édé— 47 '. (a) a“: I TC») :11”th (— a} I 1(a) <7 Page 2 ofll 2. [10] Use substitution to evaluate the definite integral: [71;— exp(—\/;)dx Page 3 ofll 3. [10] Use integration by parts to evaluate the integral: ie‘cosxdx :I’ 0 ’7g 0 Qvé /;/Q.Ay]\/\Z r - _ a: 1,0 9‘5’v)‘ QZX‘ - L("5 V: Y J of ’ CIV:_€7‘C/Y A e A V I: [UAW UV» va1\/ : .Q a»? C _ f€/—/Ew7 0’ ¥ % 17° 0 >6 “W4 JR @ 57/ (I) e 6 ‘ a v- CZ)‘ “F: /§W¥—€Yu{v: (501%)“ J -€ ) 0 Vat/U:- 3<>>Y4¥ V: ’9! g "/c mi,’ ,_ a, it, ,,,,,_,,,,,,$C _, i ,i , 7 7 : kKfif —~ [EWMY CI" / W 7 I 3? . 3 ~ e N. l’/ 9‘ 7' u \L —- .1 m M Hm ) .97 ’7 '7 4:3 m/ (a (jet i:§€¥/&wx+3&Y>/fl:” 6’ 3*; 4 f Page 4 of 11 4. [10] Use integration by parts to evaluate the indefinite integral: Ilenxdx :Z in K g cm: {Ax 12$ .24»! F) \/ t L3 I Z. i _ YA (12] _ — a V», x- 3 3 kg _3i E in , i n 3‘. —l.—{L x146 3 A; a % 3 3 "EAX‘iX 46 Page 5 of 11 5.[10] First make an appropriate substitution, and then use integration by parts to evaluate the indefinite integral: [smfidx [~— 7 K 2 X187 /' Fe/ Q/x; 2g RT: J51.) : 'Ju: =15? (2/ ("o/(Ciggji 2‘” é VT”? I— 2 [gfiMJJ‘V'Qj] le Page6 ofll 6. [10] Use the partial fraction decomposition to evaluate the indefinite integral: (Hint: see the question #7) Page 7 of 11 7. a) [5] Find A and B so that 1 _ A + B (x—1)(x+2) x—l x+2 b) [5] Use the partial fraction decomposition in a) to evaluate: 1 4% J‘(x —1)(x + 2) alum/LAMB) + P>/¥~/} :11 (nflwem avg—=4 /,\(A+B)X_F/2/( 491:1 ‘2 4- 5:4 It: // (I\}++B:fl -_~ @3730; I k *f * affair ~ WW A-éJw—wjr — 45 / K ~ cl¥ + f ) T{¥~/){;:j — f6") &/ @ifltwl— 1% [4/“9/7‘ 6 A “3 a i :1: l + 6 Page 8 ofll Page 9 ofll 9. [10] Explain why the given integral is improper, and evaluate the integral: I 270/ j 9" -372 [xii/v ’, [email protected] [IX X: Kiwi / ~ J 4 fl //x) / §x%§fog"e/KZ/, : g(:”2!fi_ Page 10 ofll 3x—2y+z=2 THE END Page 11 of 11 Total marks are 100. ...
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1505 2006 TEST 4 - YORK UNIVERSITY FACULTY OF ARTS...

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