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Unformatted text preview: Z 1 ln(1 + e x ) dx . Find bounds on the error of the approximation. 5. (16 pts.) Improper Integrals: For each of the following, tell whether the given integral converges or diverges, and if it converges, compute its value. (a) Z cos( x ) dx (b) Z 3 1 x dx 6. (16 pts.) Proofs: Prove the following: (a) Z x n e x dx = x n e x-n Z x n-1 e x dx (b) For any cubic polynomial f , given by f ( x ) = c + c 1 x + c 2 x 2 + c 3 x 3 , the Simpsons rule approximation to R b a f ( x ) dx is exact....
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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