Math 132 Exam 2 Fall 2016 15 multiple choice questions worth 5 points each 2 hand graded questions worth 12 and 13 points each Exam covers sections 6 3 6 5 7 1 7 5 7 8 8 1 8 2 No calculators For the multiple choice questions mark your answer on the answer card Show all your work for the written problems Your ability to make your solution clear will be part of the grade Useful Formulas Pn i 1 Pn i 1 i3 Pn n n 1 2 i n n 1 2 i 1 2 i2 n n 1 2n 1 6 sin2 cos2 1 1 tan2 sec2 1 cot2 csc2 sin A B sin A cos B sin B cos A cos A B cos A cos B sin A sin B tan A B cos A cos B R 1 2 tan A tan B 1 tan A tan B cos A B cos A B sin A sin B 1 2 cos A B cos A B sin A cos B 1 2 sin A B cos A B sin2 x 12 1 cos 2x cos2 x 21 1 cos 2x sin 2 2 sin cos cos 2 cos2 sin2 csc x dx ln csc x cot x C R sec x dx ln sec x tan x C Math 132 Exam 2 Z 1 Suppose you know that Z 5 f x dx Find 3 f x dx 12 and the average value of f x on 3 5 is 6 0 0 A 0 B 2 C 3 D 6 E 8 F 9 G 12 2 Find the average value of f x sin x e1 cos x on the interval 0 A e2 e 1 e e 1 B 2 2 C e e2 1 D 2 e 1 E 2 2 F e 1 e 1 G Page 2 of 11 Math 132 Exam 2 Z 3 Evaluate the definite integral 12 sin2 x cos2 x dx 0 A 48 B 48 3 32 1 64 96 643 96 1 12 24 3 96 64 24 C D E F G H 1 64 3 64 4 If you are going evaluate the integral Z x3 dx x2 6x 13 using trig substitution which substitution should you use A x 3 sin 2 B x 23 sec C x 3 tan 6 D x 2 tan 3 E x 9 sec 3 F x 2 sin 3 G x 23 tan H x 3 sec 6 Page 3 of 11 Math 132 Exam 2 Page 4 of 11 5 Identify the form of the partial fraction decomposition of the rational function 3x2 10 x2 x4 25 A B C D E F G A x A x A x A x A x A x A x Bx C x4 25 Bx C Dx E 2 x2 5 x 5 B C Dx E F x 2 2 x2 x 5 x 5 B D E Fx C x2 x 5 x 5 x2 5 B C D E Fx 2 2 x x 5 x 5 x 5 B Cx D Ex 2 2 2 x x 5 x 5 B C D E x2 x 5 x 5 x2 5 6 Use polynomial long division to write 2x4 x3 3x2 4x 9 p x Q x 2 2 x x x x where Q x and p x are polynomials What is p 2 A 0 B 1 2 C 1 D 2 E 3 F 4 G 6 Math 132 Exam 2 Z 1 7 Evaluate the integral dx 2 x 16 x 4 ln x x2 16 C A arcsin 4 x B ln 4 x2 16 C x x2 16 C ln C 4 4 x D arcsec 4 ln x x2 16 C 4 1 E ln x C x2 16 x2 16 x C F 4 4 3 2 2 G x 16 2 C 3 Z 8 Evaluate the integral x ln x dx A C B ln x C C D E F G 2 3 2 x C 3 2 3 2 x ln x 3 ln x C x C 2 3 2 x ln x 32 3 1 x3 2 C x C Page 5 of 11 Math 132 Exam 2 Page 6 of 11 Z 9 Evaluate the following improper integral or conclude that it diverges A e 0 2 e x dx x 2 B e 2 2 C 2 2 e 2 1 2 D e 2 2 2 1 E 2e F 2 e 2 1 G Diverges Z 10 Evaluate the following improper integral or conclude that it diverges A 0 B 1 2 C 1 D 2 E 4 F 6 G 8 H Diverges x2 x dx 1 Math 132 Exam 2 Z 11 Compute the following improper integral Page 7 of 11 xe x dx 0 A 1 B C D 0 E e 1 F e1 G 2e 1 H Diverges 12 Let R be the region in the half plane x 0 bounded by the curves y 3x 3 y x2 1 x 0 Compute the volume of the solid of revolution formed by rotating R about the vertical line x 1 A B C D E F G 35 6 3 2 13 3 37 5 35 12 181 15 Math 132 Exam 2 Page 8 of 11 13 The region between x 1 y 2 and x 0 is revolved around the horizontal line y 3 to form a solid Which of the following integrals represents the volume of the solid Z 1 1 y 2 3 y dy A 2 0 Z 1 1 y 2 3 y dy B 2 1 1 Z 3 1 y 2 y dy C 2 0 Z 1 1 y 2 y dy D 2 1 1 3 x 1 x dx Z E 2 0 Z 1 3x 1 x dx 1 x 1 x dx F 2 0 Z G 2 1 14 Find the length of the curve f y ln cos y for 0 y 3 A B 3 C 2 3 D ln 3 E ln 53 1 F ln 53 G ln 2 3 Math 132 Exam 2 Page 9 of 11 15 The curve y 4x 2 between x 1 and x 2 is rotated about the x axis to form a surface Compute the area of the resulting surface A 8 15 B 30 5 C 32 17 D 6 5 E 16 3 F 8 17 G 16 17 Math 132 Exam 2 Page 10 of 11 Name ID Discussion Section Letter You can find your discussion section on the front of your exam book Written Problem You will be graded on the readability of your work Use the back of this sheet if necessary 16 a 7 pts Find the partial fraction decomposition of Z b 5 pts Evaluate the integral x4 16 dx 16 16 x4 16 Math 132 Exam 2 Page 11 of 11 Name …
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