spring03 midterm

# Thomas' Calculus: Early Transcendentals

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Name Instructor Your class time MATH 104 - MIDTERM EXAM Thursday March 13, 2003, 7:30PM-9:00PM McDonnell A02 This examination booklet contains 9 problems on 10 sheets of paper including the front cover. Do all of your work in this booklet and show all your computations. This is a closed book exam. Calculators are NOT allowed. This exam was designed so that all problems could be solved without heavy computations. Problem Possible score Your score 1 12 2 12 3 12 4 12 5 12 6 12 7 12 8 6 9 10 Total 100 WRITE OUT AND SIGN PLEDGE: I pledge my honor that I have not violated the Honor Code during this examination. GRADES CAN BE OBTAINED ON THE WEB, AT THE BLACKBOARD WEB SITE FOR THE COURSE.

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1. (12 points) Find Z sin 3 (ln x ) cos 2 (ln x ) x dx .
2. (12 points) Find Z ln( x 2 + x + 1) x 2 dx .

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3. (12 points) Find Z e 3 x arctan( e x ) dx .
4. (12 points) Find Z 2 0 dx x 2 + 4 x .

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5. (12 points)

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Unformatted text preview: Find Z sin 2 θ cos 3 θ dθ . 6. (12 points) Set up an integral for the area of the region enclosed between the curve y = x 3-2 and its tangent line at x =-1. JUST SET UP THE INTEGRAL. DO NOT COMPUTE A NUMERICAL VALUE. 7. (12 points) The region R is bounded by the curves y = ln x , y = 0 and x = e . The solid S is obtained by revolving R around the y-axis. (a) Set up an integral for the volume of S using the shell method. (b) Set up an integral for the volume of S using the disk or washer method. (c) Compute the volume of S . 8. (6 points) Sketch the curve given in polar coordinates by r = 1 + sin θ . 9. (10 points) Find the length of the curve y = e x + e-x 2 as x runs from 0 to 1....
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spring03 midterm - Find Z sin 2 θ cos 3 θ dθ 6(12 points...

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