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exam2_wi04 - 3(4 points Determine if the integral Z 9 1...

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Name: Section Number: TA Name: Section Time: Math 10B. Midterm Exam 2 February 26, 2004 Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers. Write your solutions clearly and legibly. No credit will be given for illegible solutions. 1. (4 points) Let f ( x ) = x sin( x 2 ) on [0 , π ]. Find f ave , the average value of f on [0 , π ]. # Score 1 2 3 4 5 Σ
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2. (4 points) Evaluate the integral π 4 0 x sin(2 x ) dx. Show all of the steps in the calculation.
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Unformatted text preview: 3. (4 points) Determine if the integral Z 9 1 dx (9-x ) 1 3 converges or diverges; if it converges, compute its value. 4. (4 points) The region bounded by y = sin( x ), y = 0, x = 0, and x = π is rotated about the x-axis. Find the volume of the resulting solid. 5. (4 points) Estimate Z 5 1 q √ x-1 dx using the Trapezoidal Rule with two subintervals ( n = 2). You need not simplify the resulting expression....
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