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# Test 1 - y = x 3 and y = x Cross-sections perpendicular to...

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Test time = 8:30 11:30 (+5 points, if you circle the correct one) MAT 200 Fall 2006, Exam 1, Sept 26, Name (+5 points if your name is printed legibly) Style (Maximum of +5 points) 1. (+10 points) The speed of a roller coaster is measured at 1-minute intervals and is given in the table below. Estimate the distance traveled (in feet) during the 3 minutes that data was recorded. t (minutes) 0 1 2 3 v ( t ) (feet/minute) 50 47 46 40 2. (+10 points) Use the form of the definition of the integral to evaluate the integral ( 29 2 1 2 3 x dx - -

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Page 2 of 4 3. Evaluate the integrals. (+5 points for each integral) a. 1 x dx x + b. 2 2 4 x dx x x + + c. /3 x xe dx v d. 2 ln x dx x v
Page 3 of 4 4. a. (+10 points) Find the area enclosed by the curves y = x 3 and y = x . b. The base of a sculpture is the area enclosed by the curves

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Unformatted text preview: y = x 3 and y = x . Cross-sections perpendicular to the x-axis are semicircles. i. (+5 points) Draw a diagram of the sculpture. Show the base and a typical cross-section. Label the elements of your diagram appropriately. ii. (+5 points) Find the volume of the solid S . Page 4 of 4 5. (+10 points) Find the volume of the solid generated by rotating the region bounded by the given curves about the y-axis. y = x 2 , y = 3 x 6. (+10 points) On a certain website, the popularity of a recently posted video is modeled by the function P( t ) = 10 e – t /24 , t hours after it is posted. What is the average popularity during the first week it is posted to the website?...
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Test 1 - y = x 3 and y = x Cross-sections perpendicular to...

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