32B(W08)_Midterm2_Solutions

32B(W08)_Midterm2_Solutions - MATH 32B - Lecture 4 - Winter...

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Unformatted text preview: MATH 32B - Lecture 4 - Winter 2008 Midterm 2 Solutions - March 3, 2008 NAME: STUDENT ID #: DISCUSSION SECTION: This is a closed-book and closed-note examination. Calculators are not allowed. Please show all your work. Use only the paper provided. You may write on the back if you need more space, but clearly indicate this on the front. There are 6 problems for a total of 100 points. 1 2 1.(15 points) Evaluate R C F dr where F ( x,y,z ) = x yz i + y xz j + 8 z xy k and C is parameterized by r ( t ) = cos t i + sin t j + cos t k for / 6 t / 3. Solution. Remember the formula, plug in the values, compute the dot prod- uct, and party like its 31A: Z C F dr = Z b a F ( r ( t )) r ( t ) dt = Z / 3 / 6 cos t sin t cos t i + sin t cos t cos t j + 8cos t cos t sin t k (- sin t i + cos t j- sin t k ) dt = Z / 3 / 6- 1 + tan t +- 8 dt =- 3 2 + 1 2 ln3 / 3 2.(15 points) Use Greens Theorem to evaluate the line integral Z C (arctan x + y 2 ) dx + (ln 2 y- x 2...
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This note was uploaded on 05/01/2008 for the course MATH 32B taught by Professor Rogawski during the Winter '08 term at UCLA.

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32B(W08)_Midterm2_Solutions - MATH 32B - Lecture 4 - Winter...

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