MATH 2263 Midterm: MATH 2263 UMN Exam 2 SolutionsSpring 08

• School: UMN
• Department: Mathematics
• Course: MATH 2263
• Professor: All

Document Summary

April 3, 2008: (10 points) let r be the rectangle 0 x ln 7, 0 y ln 3. Solution: ex+2y = exe2y, so rrr ex+2y da = r ln 3. 2 (9 1)(7 1) = 24. y=0 hexiln 7. 0 ex dx : (10 points) let r be the square 2 x 2, 2 y 2 in the (x, y)-plane. If a continuous function f (x, y) satis es. Solution: in general, if f (x, y) g(x, y), then rrr f (x, y) da rrr g(x, y) da. So use this twice, rst with f (x, y) = 0 and g(x, y) = f (x, y), and second with f (x, y) = f (x, y) and g(x, y) = |x|. You compute rrr |x| da = r 2. 0 x dx = 16, and of course. 2r 2 f (x, y) da 16.