MATH 2E Quiz: MATH2E_Quiz4_2014Spring_Solutions
Document Summary
Partial credit will be given: (10 points) (a) evaluate the line integral by using parametric equations. C is the rectangle with vertices (0, 0), (5, 0), (5, 2) and (0, 2) oriented counterclockwise. (b) evaluate the same line integral by using green"s theorem. Solution. (a) c1 : x = t, y = 0, 0 t 5 dx = dt, dy = 0dt ; C2 : x = 5, y = t, 0 t 2 dx = 0dt, dy = dt ; C3 : x = 5 t, y = 2, 0 t 5 dx = dt, dy = 0dt ; C4 : x = 0, y = 2 t, 0 t 2 dx = 0dt, dy = dt ; C cos ydx + x2 sin ydy = cos ydx + x2 sin ydy. Z 2 (b) the region d enclosed by c is [0, 5] [0, 2], so. C cos ydx + x2 sin ydy = (x2 sin y) .
