Question 5 Evaluate where is each of the following contour. (a) is the path from (1,...
4. Evaluate the following integrals: f, where contour γ is a circle of radius 2 centered at the origin. z.İ f, -1-i,1-i,1+i,and-1+i. (z-0.1-1); where contour γ is the square with the four vertices ill) Jo (2+7 cos(e)) 4. Evaluate the following integrals: f, where contour γ is a circle of radius 2 centered at the origin. z.İ f, -1-i,1-i,1+i,and-1+i. (z-0.1-1); where contour γ is the square with the four vertices ill) Jo (2+7 cos(e))
4. Evaluate the following integrals: f, where contour γ is a circle of radius 2 centered at the origin. z.İ f, -1-i,1-i,1+i,and-1+i. (z-0.1-1); where contour γ is the square with the four vertices ill) Jo (2+7 cos(e)) 4. Evaluate the following integrals: f, where contour γ is a circle of radius 2 centered at the origin. z.İ f, -1-i,1-i,1+i,and-1+i. (z-0.1-1); where contour γ is the square with the four vertices ill) Jo (2+7 cos(e))
Evaluate the integral 5. Ten dz, where C is the boundary of the square with vertices at the points 0, 1, 1+i and i, with a counter clockwise orientation. What is the integral over the reverse contour?
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...
1. Evaluate the integrals: (a) S (x2 - y²)dz, where is the straight line from 0 to i. (b) e dz, where y is the circle of radius 1 centered at 2 traveled counterclockwise.
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.
Find parameterisations x(t), y(t), t є 1 (a) (b) (c) for each of the following curves: 2. The straight line from 4+2i to 3+5i; The circle of radius 2 centered at 3-i oriented counter-clockwise; The graph of the cosine function over the interval [π/4,2n Find parameterisations x(t), y(t), t є 1 (a) (b) (c) for each of the following curves: 2. The straight line from 4+2i to 3+5i; The circle of radius 2 centered at 3-i oriented counter-clockwise; The graph...
3. Let (a) Show that F is conservative in R3. (b) Let T denote the triangular path with vertices (1,1,1), (2,1,1) and (3,2,2), traversed from ,1) to (2,1,1) to (3,2,2) to (1,1,1). Evaluate F.dr Justify your answer (c) Find a function p: R3R such that F Vp. (d) Evaluate dr, where Г is the path y-12, z-0, from (0,0,0) to (2,4,0) followed by the line seqment from (2, 4,0 to 1, 1,2) 3. Let (a) Show that F is conservative...
A particle moves on a counter clockwise, origin-centered circular path in the x y-plane at a constant rate. The radius of the circle is r, the mass of the particle is m, and the particle completes one revolu tion in time τ a) Neatly draw the following things 1. The path of the particle 2. A dot on the path when the particle is at 00 90° and 210° where 0 is mea sured from the x-axis (posi tive counter-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. (10 pts) Evaluate where C is the boundary of the square with vertices (0,0), (1,0),(0,1) and (1, 1) oriented clockwise.