62 Select the correct answer. Which integral resembles 3| 2(3x+) dix ? O A. Judy = uv - vou OB. un+1 Jundu = +C.n # -1 n +1 OC. [e" du = e" +C OD. [a"du = . + 0 In a63 Identify the most appropriate method of integration that should be used to solve the integral stexdx . A. Integration by parts B. Partial Fraction Decomposition C. Basic Substitution D. Trigonometric Substitution 64 Select the correct answer. Evaluate the Integral X- - X dx using the appropriate strategy of integration. x + 1 O A. NI - (-5x +4In| x +1/)+C O B. NI - -(-4x + x2 + In/ x +1/)+c O C. - 8x + 2x2 + 8In| x+1/+0 OD. NI - x2 - 2x + 2In| x +1/+065 Select the correct answer. The velocity function of a person driving in a car from home to the office can be given by 11(1) = 947 .The person takes 2 hours to reach ofce. Estimate the distance between the person's home and ofce. Use Simpson's Rule and take n = 4. A 5.213 B 5.419 C. 5.353 D 5.379 66 Select the correct answer. 3 Approximate the integral I(Sin)dx using Trapezoidal rule, where n = 4. 1 A. 1.921 B. 1.931 C. 1.827 D. 1.884 67 Select the correct answer. Which statement best describes why [ax will converge or diverge? , x + A. It will converge because the corresponding limit does not exist. B. It will diverge, because the corresponding limit does not exist. C. It will converge, because the corresponding limit exists. D. It will diverge because the corresponding limit exists. 68 Select the correct answer. Which integral will converge? O A. O B. [ x -2 dx O C. ax OX+5 OD. 1 dx 3 VX - 369 Select the correct answer. Ayoung kid watches a squirrel walk continuously along a branch of a tree for 1 minute. The shape of the branch can be given by the functior 2 {(0 =13 . Find the length (in meters) traced by the squirrel along the tree. A. 1.521 m B. 1.040 m C. 1.092 m \" D. 1.624 m 70 Select the correct answer. 2 Find the length of the curve described by the function y = 14.x where, 0 5 x s 1. A. 3.462 B. 1.121 C. 1.010 D. 2.431 71 Select the correct answer. Which of the following is the area of the surface obtained by rotating the curve x = 1'25 - y2 _ 0 s y 5% . about the y-axis? A. 5 ' " B. 9 71' C. 15 72' D. 25 7: 72 Select the correct answer. An engineering student wants to find the area of surface obtained by rotating the curve y= 3x2 over the interval [0, 2], about the xaxis. Which of the following is the correct surface area? A. 455.50 B. 50.77 " C. 29.04 " D. 2,297.30 73 Select the correct answer. Find the center of mass of the system of objects that have masses 1 , 1 and 1 at the point (-2,2), (2,1) and (3,3) respectively " A. (1, 2) B. (2, 6) " C. (1, 6) " D. (3, 6) 74 Select the correct answer. The dye dilution method is used to estimate cardiac output using 7 mg of dye. The dye concentration is modeled by the function C(t) = 2t(4 - t). The dye concentration is expressed in mg/L and tis measured in seconds. Estimate the cardiac output for the time interval [0, 4]. \" A. 21.33 " B. 27.43 x C. 129.33 \" D. 0.328 75 Select the correct answer. The demand function for toy planes sold by a leading store is given as otx) = 36 - 3x, where xis the product quantity. The supply function for the same is given as 5(X) = 6X. For the given supply and demand functions, determine the equilibrium price. A. $23 B. $24 C. $26 \" D. $27 76 Select the correct answer. The marginal cost function for manufacturing perfume is given by c()() = 7X+ 28. where XiS the product quantity. Find the change in the cost of perfume when the number of units sold changes from 2 to 10, ' A. $56 ' B. $57 ' C. $62 ' D. $67 77 Select the correct answer. The average lifetime ofa light bulb is 6000 hours. What is probability that the bulb will last for more than 3000 hours? -x Note: PM 5 X 5 b) = J'blemdx where p is the average value. 3!! " A. 0.3935 " B. 0.5462 \" C. 06065 " D. 0.6487 78 Select the correct answer. For what constant k is f(x) = ke (3*+2) a probability density function on [0 1]? O A. 21.00 O B. 23.33 O C. 36.33 O D. 40.00