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408CF09assign7 - t ≤ 3 The position of the object at time...

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M408C Fall 2009 Assignment 7 Due Thursday, October 29 You should have read and understood sections 5.3, 5.4, 5.5, and 6.1 before completing this assignment. You must show sufficient work in order to receive full credit for a problem. Please write legibly and label the problems clearly. Circle your answers when appropriate. Multiple papers must be stapled together. Write your name and the time of your discussion section on each page. Feel free to discuss these problems with your classmates. However, each student must write up his or her own solution. 1. An object moves along a coordinate line with velocity v ( t ) = (2 t - 1) 2 - 1 for 0
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Unformatted text preview: t ≤ 3. The position of the object at time t = 0 is one unit to the left of the origin. (a) Find the position of the object when t = 3. (b) Find the total distance traveled by the object during those three seconds. 2. Evaluate the definite integral Z π 4 sec 2 ( x ) √ 1 + 3tan x dx . 3. Find the indefinite integral Z t 2 √ 1-tdt . 4. Sketch the region bounded by the curves y = sin x and y = sin2 x for 0 ≤ x ≤ π and find its area. 5. Sketch the region bounded by the curves y = x 2 and y = 4. This region is divided into two subregions of equal area by the line y = c . Find c ....
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