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MATH_200_spring_07_final__with_solutions

# MATH_200_spring_07_final__with_solutions - Recitation...

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Unformatted text preview: Recitation # Recitation Day/Time P Pt Sc. la 13 Final Examination Wednesday, June 13th, 2007 it) 1% PARTIAL credit may be given where appropriate, so show all your work and 3a 10 justify your answers where appropriate. 3b 6 THIS is a closed book exam. NO calculators. 4 15 WHEN the announcement is made that the exam is over, STOP writing 5 15 immediately. GOOD LUCK!!! 6a 2 6b 2 In this problem, you are supposed to evaluate (in two ways) the double integral 6c 2 ”(x2 — xy + 2y2) dA, where R is the rectangle given by 1 < x < 2, 0 < y <1 6d 2 R 6e 2 6f 2 1 a) Do this as an iterated integral, with the y integration ﬁrst, the x integration 6g 2 second. 1 7a 4 X __ L Y — _ 7b 4 ’— 7c 2 7. Total ._ :— < )4 X ”A +— L g, \ 5/3 /X y: D a— 2 1— L .3 L (X ”-Yg +b?"\dg: X g_x'a, 4.2'3’ 7— 5 a: a L Y 2_ .— —_ 4 ___ L J L z. 5 L X — Y 4.— 1”— j —— X X Z T 3 K — \— — " ' 4— ~>< s 4 5 / MATH 200 Spring 2007 Name Circle one: Lecture: 3:00 A 9:00 B 12:30 D 2:00 E 1 b) Do this as an iterated integral, with the x integration ﬁrst, the y integration second. M M’L/J L X22. 3 Z S (XLﬂngL%L3Ax:%’__7—g+lgzx/ Page 2 x2 2 Evaluate the double integral ”6 dA, where T is the triangle with vertices (0,0), T (2,0), (2,1). Hex2+y2 dA Consider the double integral , where R is the region described by Page 4 (D 3 b) Write the integral as a sum of three iterated integrals in rec an u ar c or 1na es NOT EVALUATE THE INTEGRALS! To? 4. Evaluate the it aeintd mtlerag azl 1y: 22 227\$ )6} I Jxey sin(z)dzdydx x==zOyO -7r 2:2Tr X=i g :L :8 X 8 6V} 8 SM/ﬂdﬂZ— ﬁg, /9( ”3° 7” Lg / km 9 _~Cos(a ::__£1 “(Al X30 7:0 33* z o : '1 63(3w :EJ\ 8 _e = #2,) 62 27] hr xai Wm M nix jaw/Ml: A 5. Rewrite the triple integral IIIOC + 3y)dV , where G is the region in space deﬁned G by x+y+z£l, x20, yZO, 220 as a triple iterated integral. DO NOT EVALUATE THE INTEGRAL. Page 7 6. The goal of this multipart problem is compute the double integral [0] I) .Hkx + y)2 Sll’l(x — y) dA , where R is the square in the plane with V“ R (L, A l, l. l/ / (1,0), (1,2), (0,1).ou will use change of variable for this problem. 6 a) Find the equations for the four line segments which are the edges of the square R. l m: 4—! :4_ 3—(Ci/X‘D\ @ N: (a: : .4. 3'03.’L[x,_m 21:79.1 6 b) Write the equations for the edges in level curve form f (x, y): c CE \$r><= @ am: Page 8 6 c) Find new variables u and v in terms of x and y. Q:\g4x V": ‘g—fX 6 d) Solve for x and y in terms of u and v. UH—V : 7J3 Mﬂv:;;< X: E Page 9 6 f) Write the double integral as an iterated integral with respect to the new variables u and v. DO NOT EVALUATE IT. \134 [A35 _. \ MlSl/l (”VB 0l\/ dl/L (A:l V: _1 Page 10 6 g) NOW, Evaluate the new integral. ‘ V:L Page 11 I l 7 a) Write x and y in terms of r and 6, and compute the J acobian determinant for the change of variable from x, y, to m9 . X; News U: ‘5'” Yr Xe cub i8” 36 5,46 r1055- ,—(§/4 b ‘ l : r6069 +fg’4282 F / 7 b) Write r and 6 in terms of x and y, compute the J acobian determinant for the change of variable from m9 to x, y. XL4'3L x2481. : —— 7 c) In words, what is relation between the 0 answers that you get in a) and b)? 11th ME ammgc 4 L5 Page 12 W272 :4. r BLANK -- BUT DO NOT REMOVE! Page 13 BLANK-- BUT DO NOT REMOVE! Page 14 ...
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MATH_200_spring_07_final__with_solutions - Recitation...

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