Please answer all the questions attached.

Question 2(Multiple Choice Worth 4 points) Suppose g(x)dx =13, and fg(x)dx =-3, find the value of 2+ g(x)dx. 2 O 16 O 18 0 8 O 32 Question 4(Multiple Choice Worth 4 points) Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = 1 - x2 and the x-axis? 0 [ ( 1 - x 2 )ax + 1 ( 1 - * ) ax 0 [ ( 1 - x 2 )ox - 1 ( 1 - * 2 ) ax 0 j ( 1 - x 2 ) dx 0 2 / ( 1 - * 2 ) axU Question 5(Multiple Choice Worth 4 points) 0 3 Use your graphing calculator to evaluate to three decimal places the value of J xz"x?+1 dx. -2 O 0.250 O 2.667 O 1.778 O 3.251 Question 1(Multiple Choice Worth 4 points) Which of the following integrals correctly computes the volume formed when the region bounded by the curves x2 + y2 = 25, x = 3 and y = 0 is rotated around the y-axis? On ( 25 - yz - 3 dy On V25-yz - 32 dy On 32 - ( 125 - 42 ) Jay On 25 -x2 dyU Question 2(Multiple Choice Worth 4 points) Find the volume of the solid formed by revolving the region bounded by the graphs of y = x2, x = 4, and y = 1 about the y-axis. 0 None of these 0 Question 3(Multiple Choice Worth 4 points) Use your calculator to find the approximate volume in cubic units of the solid created when the region under the curve y = cos(x) on the interval [0%] is rotated around the x-axis. O 1 O 0.785 O 2.467 03.142 1:: Question 4(Multiple Choice Worth 4 points) ii:] The base of a solid in the region bounded by the graphs of y = e'x y = O, and x = 0, and x = 1. Cross sections of the solid perpendicular to the xaxis are semicircles. What is the volume, in cubic units, of the solid? Oi .- 16e Question 5(Multiple Choice Worth 4 points) The base of a solid in the first quadrant of the xy plane is a right triangle bounded by the coordinate axes and the line x + y = 4. Cross sections of the solid perpendicular to the base are squares. What is the volume, in cubic units, of the solid? 0 8 O w / O w 8 O 128 3Question 1(Multiple Choice Worth 4 points) An elementary student kicks a ball straight into the air with a velocity of 16 feet/sec. If acceleration due to gravity is -32 ft/sec, how many seconds after it leaves his foot will it take the ball to reach its highest point? Assume the position at time t = 0 is 0 feet. O 1.25 0 6 O 0.50 O Cannot be determinedQuestion 2(Multiple Choice Worth 4 points) Find the average value of f(x) = _ over the interval [e, 2e]. O In (2) O Ln2 O Ln3it Question 3(Multiple Choice Worth 4 points) Find the distance, in feet, a particle travels in its rst 2 seconds of travel, if it moves according to the velocity equation v(t)= 6t2 - 18t + 12 (in feet/sec). "U Question 4(Multiple Choice Worth 4 points) For an object whose velocity in lsec is given by v(t) = -t2 + 6, what is its displacement, in feet, on the interval t = 0 to t = 3 secs? 0 9.000 O 9.000 0 10.596 0 -3.00 Question 5(Multiple Choice Worth 4 points) Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = cos(t) - sin(t) and V(0) = 3' O v(t) = sin(t) + cos(t) + 3 O v(t) = sin(t) + cos(t) + 2 O v(t) = sin(t) - cos(t) + 3 O v(t) = sin(t) cos(t) + 4 [c1 Question 1(Multiple Choice Worth 4 points) Choose the appropriate table for the differential equation dy _ x+1 dx X X 0 0.5 ay 2 2 2 X 0 0.5 1 ay 7 2 X 0 0.5 ay undefined 3 2 dx O Cannot be found without solving the differential equationQuestion 2(Multiple Choice Worth 4 points) The differential equation dy x-2 dx y-2 I. produces a slope field with horizontal tangents at y = 2 Il. produces a slope field with vertical tangents at y = 2 Ill. produces a slope field with columns of parallel segments OI only O Il only O l and II O Ill onlyQuestion 3(Multiple Choice Worth 4 points) Which of the following differential equations is consistent with the following slope field? tit dy O X1Q X /Q =X2 y O X1QQuestion 4(Multiple Choice Worth 4 points) A differential equation that is a function of y only 0 will produce a slope field with parallel tangents along the diagonal Q will produce a slope field that does not have rows or columns of parallel tangents Q will produce a slope field with rows of parallel tangents Q will produce a slope field with columns of parallel tangents 1:: Question 5(Multiple Choice Worth 4 points) . . . g: x The differential equation dx 7-. I. will have a slope eld with negative slopes in quadrant | II. will have a slope eld with positive slopes in all quadrants III. will produce a slope eld with columns of parallel tangents O | only 0 || only 0 I" only 0 None of these [:1