Calc Multiple Choice.
1.  Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = sin(x), the xaxis, x = 0, and x = π (4 points)  

2.  Suppose , and , find the value of . (4 points)  

3.  Evaluate the integral . (4 points)  

4.  Use your graphing calculator to evaluate to three decimal places the value of . (4 points)  

5.  (4 points)  


1.  Find the average value of f(x)=e2x over the interval [2, 4]. (4 points)  

2.  Find the velocity, v(t), for an object moving along the xaxis if the acceleration, a(t), is a(t) = 2t + sin(t) and v(0) = 4. (4 points)  

3.  Find the distance, in feet, a particle travels in its first 4 seconds of travel, if it moves according to the velocity equation v(t)= t2 + 4 (in feet/sec). (4 points)  

4.  For an object whose velocity in ft/sec is given by v(t) = t2 + 4, what is its displacement, in feet, on the interval t = 0 to t = 3 secs? (4 points)  

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)  


1.  Which of the following is the general solution of the differential equation ? (4 points)  

2.  The slope of the tangent line to a curve at any point (x, y) on the curve is . What is the equation of the curve if (3, 1) is a point on the curve? (4 points)  

3.  The particular solution of the differential equation for which y(0) = 60 is (4 points)  

4.  The temperature of a roast varies according to Newton’s Law of Cooling: , where T is the water temperature, A is the room temperature, and k is a positive constant.
If a room temperature roast cools from 68°F to 25°F in 5 hours at freezer temperature of 20°F, how long (to the nearest hour) will it take the roast to cool to 21°F? (4 points) 


5.  Find the specific solution of the differential equation with condition y(2) = e. (4 points)  


1.  Choose the appropriate table for the differential equation . (4 points)  

2.  A differential equation that is a function of x only (4 points)  

3.  The differential equation . (4 points)
I.will have a slope field with negative slopes in quadrant I II.will have a slope field with positive slopes in all quadrants III.will produce a slope field with columns of parallel tangents 


4.  Which of the following differential equations is consistent with the following slope field?
(4 points) 


5.  The differential equation . (4 points)
I. produces a slope field with horizontal tangents at y = 4 II. produces a slope field with horizontal tangents at x = 0 III. produces a slope field with vertical tangents at x = 0 and y = 4 



1.  Which of the following values would be obtained using 10 inscribed rectangles of equal width (a lower sum) to estimate ? (4 points)  

2.  Which definite integral approximation formula is ? (4 points)  

3.  The estimated value of , using the trapezoidal rule with 4 trapezoids is (4 points)  

4.  Given the table below for selected values of f(x), use 6 trapezoids to estimate the value of
. (4 points)


5.  Function f(x) is positive, increasing and concave down on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of . Which one of the following statements is true? (4 points)  
