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sample_exam_1 - Z 1 sin( x 2 ) dx cannot be evaluated using...

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Math 227 Section 4 and 5 Sample Exam 1 double-sided sheet of notes. R 1 0 e 2 x p 1 + e 4 x dx using the substitution u = e 2 x : Make sure 2. (10 points each) Find each of the following. (a) R 6 x x 2 9 dx (b) R 3 1 x 2 ln x dx (c) R & 0 j cos x j dx (d) R e x 1 + e 2 x dx 3. (5 points) Suppose that f is a positive continuous function and g g ( x ) = Z x 0 f ( t ) dt: Must g be an increasing function of x ? Explain why or why not. 4. The integral
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Unformatted text preview: Z 1 sin( x 2 ) dx cannot be evaluated using the Fundamental Theorem of Calculus because sin( x 2 ) does not have an elementary antiderivative. (a) (10 pts) Approximate its value using Simpson±s method with n = 4 : Round your &nal answer to 4 decimal places. (b) (5 pts) You are given that & & & d 4 dx 4 sin( x 2 ) & & & ± 30 on the interval [0 ; 1] : Find an upper bound for the error in your approximation (ignoring round-o/ error). (c) (5 pts) Find the value of n that guarantees an accuracy of ² : 0001 1...
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This note was uploaded on 10/16/2011 for the course MATH 227 taught by Professor Cheung during the Spring '09 term at S.F. State.

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