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Unformatted text preview: ) x, i.e., a simpler expression which does not involve the summation symbol. Since n X k =1 f ( c k ) x = n X k =1 9724 n k48 n 2 k 2 4 n = 4 n n X k =1 9724 n k48 n 2 k 2 = 388 n n X k =1 196 n 2 n X k =1 k192 n 3 n X k =1 k 2 , we may use standard summation formulas to simplify, leading to n X k =1 f ( c k ) x = 388 n n96 n 2 1 2 n 2 + 1 2 n 192 n 3 1 3 n 3 + 1 2 n 2 + 1 6 n = 3884848 n6496 n32 n 2 = 276144 n32 n 2 , a closedform representation of the summation. (e) Finally, the area is given by Area = lim n n X k =1 f ( c k ) x = lim n n X k =1 276144 n32 n 2 = 276 . 2...
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 Fall '10
 KIHYUNHYUN
 Calculus, Angles

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