MTH132-Test4 - x f over 3 3-5[12 pts Find the area of the region enclosed by the curves 4 2 = x y and 2 6 x y-= Page 4 5[10 pts Set up a Riemann

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Page 1 10/18/2011 Name (Print Clearly): Student Number: April 27, 2009 Instructor: Dr. W. Wu Instructions: Answer the following questions in the space provided. There is more than adequate space provided to answer each question. The total time allowed for this quiz is 50 minutes. 1 [5 pts each] . Find the derivatives (FTC I). (a) = x dt t y 0 2 ) tan( (b) dt t t y x + = 0 2 2 ) 1 ( 2. [6 pts each] . Evaluate indefinite integrals. (a) + dx x x 2 3 1 6
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Page 2 10/18/2011 (b) + dx x x x 2 3 3. [7 pts each]. Evaluate the definite integrals. (a) + 1 0 3 ) 1 ( dx x (b) - 2 / 2 / 4 ) cos (sin π dx x x
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Page 3 10/18/2011 4. [12 pts] . Let 3 2 ) ( 2 - + = x x x f , 3 3 - x . (a) Compute - 3 3 ) ( dx x f (b) Find the total area enclosed by x-axis and the graph of
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Unformatted text preview: ) ( x f over ] 3 , 3 [-5 [12 pts] . Find the area of the region enclosed by the curves 4 2 + = x y and 2 6 x y-= . Page 4 10/18/2011 5. [10 pts] Set up a Riemann sum approximation to the integral ∫ + 2 2 ) 1 ( dx x by partitioning the interval ] 2 , [ into 4 subintervals of equal length and using the left endpoint of each subinterval. (a) Evaluate this sum. (b) Sketch the graph of 1 2 + = x y over ] 2 , [ . Sketch (shade) the rectangles associated to this Riemann Sum. (c) [bonus 2pts]. Express ∑ = ∞ → ⋅ + n k x n n k 1 2 ] 1 2 [ lim as a definite integral....
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This note was uploaded on 10/17/2011 for the course MTH 133 taught by Professor Staff during the Fall '08 term at Michigan State University.

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MTH132-Test4 - x f over 3 3-5[12 pts Find the area of the region enclosed by the curves 4 2 = x y and 2 6 x y-= Page 4 5[10 pts Set up a Riemann

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