MATH 2433 - Fall 2015 Homework Week 12 Instructions Homework will NOT be accepted through email or in person. Homework must be submitted through CourseWare BEFORE the deadline. Submit the multiple choice section of the assignment at http://www.casa.uh.edu under "EMCF" and choose ehw 12. 1. Let f ( x, y= x 2 + y 2 , and let h ( x, y ) = f . What is ) h ( r ) dr where C is the closed path C that goes counterclockwise around the unit circle? a. 2 b. c. 1/2 d. 0 e. 2 f. None of these 2. Find C ydx + xdy where C is the closed path that goes counterclockwise around the rectangle with vertices (1,1), (1,4), (3,1), and (3,4). a. 12 b. 15 c. 1 d. 0 e. 3 f. None of these 3. Find y) h ( r ) dr where h ( x,= C cos( x 2 )i + ( x 3 + 3 xy 2 ) j and C is the closed path that goes counterclockwise around the unit circle. (Hint: Green's Thm and then convert to polar) a. 4 b. 2 c. 3 d. 2 e. 2 f. None of these 4. Evaluate a. b. c. d. e. f. 3 9/2 6 5/2 81/2 none of these 5. Evaluate a. b. c. d. e. f. along the line segment C from (0, 0) to (3, 1). along the curve C : 0 2 5/2 1/2 none of these 6. Evaluate along the circle centered at the origin with radius 2. a. b. c. d. 0 e. none of these 7. Evaluate a. 5/6 b. 11/6 c. 0 d. 4/3 e. none of these along the path C: from (0,0) to (1,2) 8. Evaluate a. 5/6 b. 11/6 c. 0 d. 4/3 e. none of these 9. - 10. Choose C along the path C: from (0,0) to (1,2) to (0,2) to (0,0) \f\f\f\f\f\f\f\f\f\f