Math 132 Midterm Examination 1 February 8 2012 6 multiple choice 4 long answer 100 points General Instructions Please answer the following without use of calculators You may refer to a 3x5 card but no other notes Part I of the exam is multiple choice while Part II is long answer Part I Instructions If you do not have a pencil to fill out your answer card please ask to borrow one from your proctor Write your Student ID number on the six blank lines on the top of your answer card and shade in the corresponding bubbles to the right of each digit Fill in the bubble corresponding to each of the following 6 questions Each is worth 4 points On Part I no partial credit will be given 1 Let xi 3i 1 for i 0 1 n These xi s form a partition of the interval 2n a 1 0 1 b 1 2 c 1 2 d 0 21 e 0 1 f 0 2 g 0 3 h 1 32 i 1 3 j 1 52 k None of the above 2 Which of the following is equal to 19 X 1 i 1 a 0 1 12 31 b 0 1 12 31 c 1 12 13 i 1 19 1 20 1 19 1 20 d 1 12 13 Z 19 1 dx e x 1 Z 19 1 f dx x 0 Z 20 1 g dx x 0 Z 20 1 dx h x 1 i None of the above 3 Which of the following is an antiderivative of a b c d e f g h 1 tan 1 x 4 1 tan 1 x 2 tan 1 2x 1 tan 1 2x 2 ln 1 4x2 1 ln 1 4x2 4 1 ln 1 4x2 2x 1 ln 4x2 i None of the above 1 1 4x2 d 4 dx Z x sin t2 dx is equal to a sin x2 b cos x2 c 2x sin x2 d 2x cos x2 e 0 f cos x2 C 1 g x cos x2 2 1 h x cos x2 C 2 i None of the above 5 If f is a continuous function such that R4 1 then find 0 f t dt a 4 b 3 c 2 d 1 e 0 f 1 g 2 h 3 i 4 j None of the above R 12 0 f t dt 3 R 12 2 f t dt 4 and R4 2 f t dt 6 Which of the following definite integrals have n X i 1 as an associated Riemann sum Z 2 x I 1 4 dx 2 0 R3 4 II 1 x dx R1 III 0 2 1 x 4 dx a None of the above b I only c II only d III only e I and II only f I and III only g II and III only h All of the above 1 i 4 2 n n Name Id Math 132 Part II Instructions Answer the following on the exam sheet showing all your work Correct answers without correct supporting work may not receive full credit You may use the back of each page for additional answer space please clearly indicate if you have done so or scratch work Please put your name and student id number on each page of Part II now 1 Integration Z 1 sin x dx a 5 points Evaluate 1 Z b 5 points Evaluate Z x sin x2 dx ln 3 c 5 points Evaluate e2x 1 ex dx ln 2 d 7 points Solve the initial value problem If then find f t d f t 8t 2t2 1 4 and f 0 1 dt Name Id Math 132 2 Areas and volumes a 15 points Find the volume of the object formed by rotating r x y 1 x2 about the x axis for 0 x 2 b 10 points Find the area between the curves y sin x and y cos x for 0 x 2 Name Id Math 132 3 The Fundamental Theorem of Calculus a 6 points Using definite integrals give an antiderivative of sin x2 For full credit explain clearly what theorems and or properties of sin x2 that you are using Z 2 b 8 points Find 0 d x sin x e dx dx Name Id Math 132 4 Riemann sums and definite integrals a 5 points The points 1 x0 x1 x2 xn 1 xn 3 form the uniform partition of 1 3 Find xi and give the length of each part Z b 6 points Give any Riemann sum for partition and points that you make 1 3 1 dx Be sure to explain the choice of x c 4 points In 1 3 sentences explain why the function 1 if x is rational f x 0 otherwise from Worksheet 1 is not integrable on 0 1
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