Math 132 Exam 1 Practice Questions 1 Which of the following represents the volume of the solid generated when the area of the region enclosed by y 2x and y 2x2 is rotated around the line y 3 A cid 0 3 2x 2 3 2x2 2 cid 1 dx B cid 0 3 2x2 2 3 2x 2 cid 1 dx cid 90 2 cid 32 cid 16 C 3 3 cid 18 cid 19 2 cid 33 cid 114 y 2 cid 19 2 cid 16 3 cid 33 cid 17 2 y 2 cid 17 2 y 2 cid 114 y 2 dy dy cid 90 2 cid 32 cid 18 D 3 cid 90 1 cid 90 1 0 0 0 0 A 602 C B 120 C C 524 C D 2020 C 2 Suppose that the temperature at time t is rising with a rate of 6t2 2 degrees per minute If the initial temperature if 0 C what is the tem perature after 10 minutes 1 3 O t represents the annual rate of world consumption of oil in trillions of barrels at time t where t represents years since 1999 Assuming that the world rate of consumption was 80 trillion barrels consumed before 1999 which of the following expressions represents the amount of oil consumed between 1999 and 2010 A O cid 48 11 B O t dt cid 90 11 0 C cid 82 11 0 O cid 48 t dt D 80 cid 82 11 0 O t dt 4 Evaluate the following x cid 90 d dx 1 14t9 dt A 28 3 x6 C 7x4 B 7 5x6 7 5 D 14x9 2 5 Evaluate the integral cid 90 1 cid 18 2 t t2 sin cid 19 6 dt A cos 6 C 1 2 cid 18 2 t cid 19 B cos 6 C 1 2 cid 18 2 t cid 19 C 2 cos 6 C cid 19 cid 18 2 t D cos 6 C cid 19 cid 18 2 t 2 6 Consider the region R enclosed by curves y x2 5 and y 2x 5 a Sketch the region R Find and label the intersection points b Find the area of the region in part a 4 3 c Find the volume of the solid obtained by rotating R around the x axis 24 cid 20 32 5 cid 21 88 5 Evaluate the following integrals cid 90 7 8 9 cid 90 cid 90 3 1 cid 90 x sin 1 x3 2 dx cos 1 x3 2 C 4x4 ln x dx x5 ln x x5 C x2 ln 3x dx 9 ln 9 ln 3 26 9 10 2x3 x2 4 dx x2 4 3 2 8 x2 4 C cid 112 4 5 2 3 2 3 1 3 4 25 3 11 12 13 14 15 0 cid 90 0 cid 90 cid 90 cid 90 3 tan3 sec3 d 31 5 7 3 58 15 t 25t2 1 cid 112 1 25 dt 25t2 1 C cid 90 2 cos x 2 2 sin x 3 dx 3 64 1 x2 16 x2 sin x 1 cos2 x dx x2 16 16x C dx tan 1 cos x C 16 Evaluate the integral dx ln x 1 2 ln x 2 C 17 Evaluate the integral dx x3 x2 x ln x 1 C x x2 3x 2 cid 90 cid 90 x3 x 1 1 3 1 2 4
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