Evaluate the integral 5. Ten dz, where C is the boundary of the square with vertices...
2 +1 (b) Evaluate the contour integral dz, 22 – 9 where I is the boundary of the square D = {z E C:-4 < Re(z) < 4, -4 < Im(z) < 4} traversed once counterclockwise.
(10 pts) Evaluate where C is the boundary of the square with vertices (0,0), (1,0),(0,1) and (1, 1) oriented clockwise. (10 pts) Evaluate where C is the boundary of the square with vertices (0,0), (1,0),(0,1) and (1, 1) oriented clockwise.
P1: Let the contour C denote the boundary of a square whose sides lie along the lines x = +- 2, y= +-2, running counter-clockwise. Evaluate each of these integral Let the contour C denote the boundary of a square whose sides lie along the lines x = ±2 and y 2, running counter-clockwise. Evaluate each of these integrals: cos(z) (2-%)2 cosh z Let the contour C denote the boundary of a square whose sides lie along the lines x...
Question 5 Evaluate where is each of the following contour. (a) is the path from (1, ) to (0-1) along the unit circle (centered at angin) in counter-clockwise direction. (b) C is the straight line from (1, 0) to (0-1). (c) C is the path along the square with vertices at (1.11) traversed in the clockwise direction (d) is the path along the circle of unit radius centered at (1.1) traversed in the counter-clockwise direction
Use Stokes' Theorem to evaluate fe(x+y)dx + (2x – 3)dy +(y +z)dz over the boundary of the triangle with vertices (2,0,0), (0,3,0), (0,0,6) traversed in the counter clockwise direction.
6. (1 point) Use Stokes' Theorem to find the line integral /2y dx + dy + (4-3x) dz, where C is the boundary of the triangle with vertices (0,0,0), (1,3,-2), and -2,4,5), oriented counterclockwise as viewed from the point (1, 0, 0) 6. (1 point) Use Stokes' Theorem to find the line integral /2y dx + dy + (4-3x) dz, where C is the boundary of the triangle with vertices (0,0,0), (1,3,-2), and -2,4,5), oriented counterclockwise as viewed from the...
Problem. Use Green's Theorem, to evaluate the line integral, 5. Pdr + Qdy = 1] (e. - SP) da, 1. (=x+ + e* In y)dx + (x + y + ) dy, where C is the triangle with the vertices (1,1), (2.1), and (2, 2), and the positive (counter- clockwise) orientation. (10 points)
I sinta fosinta 3. (40 points) Evaluate the following integrals: (a) (10 points) sin(2 + 7)dz, where C is the square with vertices at 2i, 3i, 1+ 3i and 1+2i, in this order. (b) (10 points) sin(22) $c 2+1 where C is the positively oriented (counter-clockwise) triangle with vertices (0,0), (2,0) and (0,5). (c) (10 points) cosh(22) -dz, (3-2) where is the negatively oriented (clockwise) circle centered at (1,1) of radius 2. (d) (10 points) dz, 2-1 where C consist...
Evaluate the integral [c F.dr. F(x, y) = (x + y) i + (3x - cos y) j where is the boundary of the region that is inside the square with vertices (0,0), (4,0),(4,4), (0,4) but is outside the rectangle with vertices (1, 1), (3,1),(3,2), (1,2). Assume that C is oriented so that the region R is on the left when the boundary is traversed in the direction of its orientation.
2. (a) Evaluate the contour integral z dz, where I is the circle 12 – 11 = 2 traversed once counterclockwise.