1. Which of the following integrals represents the area of the region bounded by x = e and the functions f(x) = ln(x) and g(x) = log1/e(x)? (4 points) 2. Which integral gives the area of the region in the first quadrant bounded by the axes, y = ex, x = ey, and the line x = 4? (4 points) 3. Find the area of the region bounded by the graphs of y = 2 - x2 and y = -x. (4 points) 4.5 1.5 -1.833 None of these 4. Find the area of the region bounded by the graphs of y = x, y = 6 - 2x, and y = 0. (4 points) 3 6 9 None of these 5. Find the number a such that the line x = a divides the region bounded by the curves x = y2 − 1 and the y-axis into 2 regions with equal area. Give your answer correct to 3 decimal places. (4 points) 1. 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, (4 points) ] is rotated around the x-axis. 1 0.785 2.467 3.142 2. 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. (4 points) None of these 3. Which of the following integrals correctly computes the volume formed when the region bounded by the curves x2 + y2 = 100, x = 6 and y = 0 is rotated around the y-axis? (4 points) 4. 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? (4 points) 8 5. The base of a solid in the region bounded by the graphs of y = e-x y = 0, and x = 0, and x = 1. Cross sections of the solid perpendicular to the x-axis are semicircles. What is the volume, in cubic units, of the solid? (4 points) 1. Find the average value of f(x) = over the interval [e, 2e]. (4 points) Ln2 Ln3 2. Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = 3t2 + cos(t) and v(0) = 2. (4 points) v(t) = t3 + sin(t) + 2 v(t) = t3 - sin(t) + 3 v(t) = 6t - sin(t) + 2 v(t) = t3 - sin(t) + 2 3. Find the distance, in meters, a particle travels in its first 10 seconds of travel, if it moves according to the velocity equation v(t)= 49 - 9.8t (in meters/sec). (4 points) -49 0 245 441 4. For an object whose velocity in ft/sec is given by v(t) = -3t2 + 5, what is its displacement, in feet, on the interval t = 0 to t = 2 secs? (4 points) 6.607 2 -2.303 2.303 5. A girls throws a tennis ball straight into the air with a velocity of 64 feet/sec. If acceleration due to gravity is -32 ft/sec2, how many seconds after it leaves the girl's hand will it take the ball to reach its highest point? Assume the position at time t = 0 is 0 feet. (4 points) 4 secs 2 secs 1 sec Cannot be determined 
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