# 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 1 0 e x dx 2. (10 points) Compute dx 1 + x 2 3. (10 points) Consider I = 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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