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Unformatted text preview: )Δ x, i.e., a simpler expression which does not involve the summation symbol. Since n X k =1 f ( c k )Δ x = n X k =1 ± 9724 n k48 n 2 k 2 ²± 4 n ² = 4 n n X k =1 ± 9724 n k48 n 2 k 2 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 )Δ x = 388 n n96 n 2 ± 1 2 n 2 + 1 2 n ²192 n 3 ± 1 3 n 3 + 1 2 n 2 + 1 6 n ² = 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 ) Δ x = lim n →∞ n X k =1 ± 276144 n32 n 2 ² = 276 . 2...
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 Fall '10
 KIHYUNHYUN
 Calculus, Angles, Harshad number, Summation, 1 k, )∆x,, 1 48 24 k

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