c2e1 - K ( b-a ) 3 12 n 2 where K is an overestimate of the...

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Calculus II V1102 Section 007, Fall 2007 Exam 1 Name: October 2, 2007 Do all problems, in any order. Show your work. An answer alone may not receive full credit. No notes, texts, or calculators may be used on this exam. Problem Possible Points Points Earned 1 10 2 10 3 10 4 14 5 10 6 10 7 10 TOTAL 74 1
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1. (10 points) Compute Z 1 0 e x dx 2. (10 points) Compute Z dx 1 + x 2 3. (10 points) Consider I = Z 3 0 ( x 3 + 1) 7 / 2 dx . Find n (the number of subdivisions) so that the Trapezoidal Rule estimate of I will be within 10 - 6 of the true value of the definite integral. (You may use the error bound
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Unformatted text preview: K ( b-a ) 3 12 n 2 where K is an overestimate of the magnitude of the second derivative.) DO NOT COMPUTE THE TRAPEZOIDAL ESTIMATE! 4. (14 points) Using the method of partial fractions, show that Z x 2 x 3 + x 2 + x + 1 dx = 1 2 ln(( x + 1) √ x 2 + 1)-1 2 arctan x . 5. (10 points) Compute Z 1 e 2 x e x + 1 dx 6. (10 points) Compute Z π sin 5 x dx . 7. (10 points) Compute Z 4 3 √ x 2-2 x dx . 2...
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This note was uploaded on 10/18/2011 for the course MATH V1102 taught by Professor Mosina during the Fall '08 term at Columbia.

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c2e1 - K ( b-a ) 3 12 n 2 where K is an overestimate of the...

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