32B(W08)_PracticeMidterm2_Solutions

# 32B(W08)_PracticeMidterm2_Solutions - MATH 32B - Lecture 4...

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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 the line integral Z C 2 xye x 2 dx + e x 2 dy over a path C from (0,1) to (1,3). Solution. We note that this is an integral of the form R C F dr , where F ( x,y ) = 2 xye x 2 i + e x 2 j . But F is a conservative vector field since: y (2 xye x 2 ) = 2 xe x 2 = x ( e x 2 ) (We should also note that this function, 2 xe x 2 , is continuous for all ( x,y ), so F is conservative over the entire plane.) Now it is easy to see that F = f , where f ( x,y ) = ye x 2 . Therefore, Z C 2 xye x 2 dx + e x 2 dy = Z C F dr = f (1 , 3)- f (0 , 1) = 3 e- 1 / 3 2.(15 points) Find the work done by the force field...
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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)_PracticeMidterm2_Solutions - MATH 32B - Lecture 4...

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