MATH 132 EXAM II FALL 2010 This exam should have 18 questions Part I will have 16 multiple choice questions 5 points each Part II will have 2 hand graded questions 10 points each Please check to to see that your exam is complete If you do not have a pencil to mark your card please ask to borow one from your proctor Write your ID NUMBER not your SS number on the six blank lines on the top of your answer card using one blank for each digit After being sure of which answer you think is right shade in the corresponding box on your card 1 Evaluate 9 B B E 9 B 9 B G F 9 B 9 B G G B 9 B G H 38 B 38 B G I 38 B 38 B G J B 38 B G K 9 B G L 9 B 9 B 38 B G M 38 B 38 B 9 B G N 38 B 9 B G 2 What is the form of the integral substitution B 38 E 38 F 9 G 38 H 9 I 38 9 J 38 9 K 38 9 L 8 M N 8 B B B after we make the trigonometric 0 2 Use partial fractions to evaluate B B B B B E 68 B G F 68 B B G G 8 B G H 8 B G I B J 68 B B G B K 68 B G B L 68 B G M 68 8 B G N 8 6 8 B G 4 Approximate B B using the Trapezoidal Rule with 8 to 4 decimal places E 5 F G H I J K L M N 0 5 How large should n be to guarantee that Simpson s Rule of approximation for B B is acurate to within 0 0001 recall EW l O 8 E F G H I J K L M N 6 Evaluate the improper integral divergent B B B if it is convergent If not say it is E F G H I J K L M N 3 1 8 0 7 A B C D E F G H I N Find the area of the region enclosed by the curves y x 8 C B B 8 Find the area of the region in the first quadrant enclosed by B C and by the lines B C B A B C D E F G H I N 0 5 9 Find the volume of the solid obtained by rotating the region bounded by the curve y 2 B and the line y x about the x axis A 1 B 15 1 G 1 H 203 1 I 1 J 23 1 K 1 L 1 M 35 1 N 1 10 Find the volume of the solid obtained by rotating the region bounded by the curve B C and the line B about the line B A 1 B 151 G 1 H 2 1 I 1 21 J K 1 L 1 M 51 N 1 0 6 Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the curve C B B and the line B C about the C axis A 1 B 1 L 1 M 1 G 1 H 2 1 N 1 I 1 J 2 1 G 1 0 7 12 Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the curve C B and the lines C B about the line C A 1 B 1 1 G 1 H 2 1 L 1 M 1 N 1 I 1 21 J K 1 0 13 Which of the following integrals gives the length of the curve B C A F G H I J K L M N 14 Find the average value of y x over the interval A F G H I J K L M N 1 3 0 15 A force of 10 lb is required to hold a spring stretched 5 inches beyond its natural length Find the amount of work done in ft lbs to stretch it from its natural length to 6 inches beyond its natural length A 1 B 2 C 3 D 4 E 5 F 6 G 7 H 8 I 9 J 10 16 Suppose 3 ft lbs of work is required to stretch a spring from 2 ft to 4 ft beyond its natural length How far in ft will a weight of 5 lb stretch the spring beyond its natural length A 20 B 18 75 C 15 D 10 E 8 F 6 25 G 5 H 3 5 I 2 J 1 5 0 PART II CLEARLY WRITE YOUR SOLUTION AND HOW YOU GOT IT Name ID Subsec 17 Consider the region in the first quadrant bounded by the curve C B and the lines B C and C a Find the area by integrating with respect to x 0 B 1 B B 5 points You might need more than one integral d b Find the area by integrating with respect to y c 0 y 1 y y 5 points Make sure you get the same answer as above 0 PART II CLEARLY WRITE YOUR SOLUTION AND HOW YOU GOT IT Name ID 1 Consider the solid obtained by rotating about the x axis y x 8 C B a Find the volume of the solid Subsec the region bounded by using the disc washer method 5 points b Now use the method of cylindrical shells to find the volume of the above solid and see that you get the same answer 5 points
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