2B_midterm1_samp - f ( x ) dx 4 1 3 , find f ( x ) x dx 1 9...

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Last Name:_______________________ First Name:_______________________ ID #:_______________________ TA:_______________________ Sample 2B Midterm Exam # 1
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1. a) (5 points) Estimate, using Riemann sums, the area under the graph of f ( x ) x 2 and above the x-axis from x 1 to x 4 by using three approximating rectangles and right-hand endpoints. b) (10 points) Find x 2 1 4 dx by using the definition of the definite integral. Is this the area we are trying to approximate in part a? Why or why not?
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2. (10 points each) Integrate a) | cos x | dx 0 3 2 b) x 3 1 x 2 dx 1 2
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c) 1 x 2 1 1 x 3 dx 3. (5 points) Find g '( x ) if g ( x ) cos x 1 d .
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4. (10 points) If f is continuous for all real numbers and
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Unformatted text preview: f ( x ) dx 4 1 3 , find f ( x ) x dx 1 9 5. a) (10 points) Find the area of the region bounded by y x 1 , y , and x 5 . b) (15 points) Find the volume of the solid generated by revolving about y 3 the region described in part a (that is, the region bounded by y x 1 , y , and x 5 .) c) (15 points) Find the volume of the solid whose is base is the region described in part a (that is, the region y x 1 , y , and x 5 ) and whose cross-sections perpendicular to the y-axis are squares with side lying in the xy-plane....
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This note was uploaded on 11/21/2010 for the course MATH CALCU Math 2B taught by Professor Alessandrapantano during the Fall '10 term at UC Irvine.

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2B_midterm1_samp - f ( x ) dx 4 1 3 , find f ( x ) x dx 1 9...

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