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Unformatted text preview: i. Write a dierential equation that is satised by y . ii. Solve the dierential equation obtained above. Leave your answer in implicit form. 4. (20 pts.) Arc Length and Surface Areas of Revolution: (a) Find the length of the curve described by y = ln(cos( x )); 0 x 4 . (b) Let f ( x ) = 1 3 ( x 2 + 2) 3 2 for 1 x 2. Approximate to 4 decimal places the area of the surface obtained by rotating the graph of f about the xaxis. 5. (20 pts.) Moments and Centers of Mass: (a) Masses m 1 ,...m 4 are located at the points P 1 ,...,P 4 , respectively, where m 1 = 3 , m 2 = 3 , m 3 = 8 and m 4 = 6, and where P 1 = (1 ,2) , P 2 = (2 , 4) , P 3 = (3 ,4) and P 4 = (6 ,5). Find their moments about the x and yaxes, and nd the center of mass of the system. (b) Find the centroid of the region bounded by the curves with equations y = x , y = 0 and x = 4....
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This note was uploaded on 01/24/2011 for the course MATH 21 taught by Professor Mathdep during the Winter '98 term at Missouri S&T.
 Winter '98
 MathDep
 Power Series

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