For each of the following, compute C a) C is the polygonal path consisting of the line segment from (1, 1) to (2, 1) followed by the line segment from (2, 1) to (2, 3), and y dx x dy b) C is the intersection of z x2 y2 and x2 y2 z2 1, oriented in the counterclockwise direction when viewed from high...

a Let C 1 represent the horizontal piece and C 2 represent the vertical piece On ...

For each of the following, compute C . a) C is the polygonal path consisting of the

Question:

For each of the following, compute ∫C ω.
a) C is the polygonal path consisting of the line segment from (1, 1) to (2, 1) followed by the line segment from (2, 1) to (2, 3), and ω = y dx + x dy.
b) C is the intersection of z = x2 + y2 and x2 + y2 + z2 = 1, oriented in the counterclockwise direction when viewed from high up the positive z-axis, and ω = dx + (x + y) dy + (x2 + xy + y2) dz.
c) C is the boundary of the rectangle R = [a, b] × [c, d], oriented in the counterclockwise direction, and ω - xy dx + (x + y) dy.
d) C is the intersection of y = x and y = z2, 0 < z < 1, oriented from left to right when viewed from far out the y-axis, and ω = √x dx + cos y dy - dz.