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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 π/ 6 ≤ t ≤ π/ 3. Solution. Remember the formula, plug in the values, compute the dot prod- uct, and party like it’s 31A: Z C F · dr = Z b a F ( r ( t )) · r ( t ) dt = Z π/ 3 π/ 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 π/ 3 π/ 6- 1 + tan t +- 8 dt =- 3 π 2 + 1 2 ln3 / 3 2.(15 points) Use Green’s Theorem to evaluate the line integral Z C (arctan x + y 2 ) dx + (ln 2 y- x 2...
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32B(W08)_Midterm2_Solutions - MATH 32B Lecture 4 Winter...

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