{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

1505 2006 TEST 4

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

This preview shows pages 1–11. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ’, «@151 [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. ...
View Full Document

{[ snackBarMessage ]}

Page1 / 11

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

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online