calc exam 3 - x + 2 x 2 + 4 x dx (d) Z x 5 1 + x 2 dx 2 5....

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Math 2144, Calculus I Name: Exam 3 July 24, 2007 This exam is a closed book exam (you may not use a calculator). The exam consists of seven problems worth 100 total points. You have 50 minutes in which to work. You must show all calculations or give explanations of your answers in order to recieve full credit. 1. (10 points) If R 9 0 f ( x ) dx = 10 and R 4 0 f ( x ) dx = 7, find R 9 4 f ( x ) dx . 2. (15 points) Estimate the area under the graph of f ( x ) = x 2 from x = 0 to x = 4 using four approximating rectangles and right endpoints. Sketch the graph and the rectangles. Is your estimate an underestimate or an overestimate? 3. (15 points) Evaluate: (a) Z π 0 d dx ± sin( x 2 ) cos( x 2 ) ² dx (b) d dx Z x 0 ± sin( t 2 ) cos( t 2 ) ² dt 1
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4. (20 points) Evaluate the following integrals, if they exist. If they do not exist, then explain why. (a) Z 1 0 (8 x 3 - 8 x + 3) dx (b) Z (1 - x ) 9 dx (c) Z
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Unformatted text preview: x + 2 x 2 + 4 x dx (d) Z x 5 1 + x 2 dx 2 5. (10 points) Find the area of the region enclosed by the parabolas y = x 2 and y = 2 x-x 2 . 6. (10 points) The region bounded by the given curves is rotated about the specied axis. Find the volume of the resulting solid by any method. (a) y = 1 x , x = 1, x = 2, y = 0; about the x-axis. (b) y = x-x 2 , y = 0; about x = 2. 3 7. (10 points) Find the average value of the function f ( x ) = x 2 on the interval [-1,1]. Extra Credit (20 points): A car braked with a constant deceleration of 16 ft/s 2 , producing skid marks measuring 200 ft before coming to a stop. How fast was the car traveling when the brakes were rst applied? 4...
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calc exam 3 - x + 2 x 2 + 4 x dx (d) Z x 5 1 + x 2 dx 2 5....

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