Let me discuss this problem part by part

![0 = (1-ig (x2+x-i-zxi +i) dx Ő 10 3 = (1-i) + -i +ix) 11 12 = (1-1) [0 - 5 - 1 +9=*] = (1-1) = (1+i) Ś (1-i) (1+i) - 1/3 (1-(](http://img.homeworklib.com/questions/e3a14d90-813e-11eb-bf64-f5aaf7b432b3.png?x-oss-process=image/resize,w_560)
Use Green's theorem to evaluate line integral F.dr, where F(x, y) = (y2 – x2)i + (x2 + y2)j, and C is a triangle bounded by y = 0, x = 6, and y = x, oriented counterclockwise.
5. Evaluate the integral of f along a contour y where f and y are given as follows. (a) f(x+iy) = eyel-ix along y, a positively oriented ellipse determined by the equation r = cos(20) +2. [6 (b) f(x) = 223(24 – 1)-2 along y(t) =t+iVt where 0) <t<1. [10]
I 8. [6 points) Evaluate the line integral, dr where F(x, y) = 2xy i + (x2 - y2); and C is where is the are of the parabola y = z from (1,1) to (2,4). (Hint: You may view C as =2 y=?,ists 2.)
5)Evaluate f (x2-y)dr + (y2 +x)dy along a) a straight line from (0.1) to (1,2), b) straight lines from (0,1) to (1,1) and then from (1,1) to (1,2), c) the parabola z t,y 1
1. Evaluate the line integral S3x2yz ds, C: x = t, y = t?, z = t3,0 st 51. 2. Evaluate the line integral Scyz dx - xz dy + xy dz , C: x = e', y = e3t, z = e-4,0 st 51. 3. Evaluate SF. dr if F(x,y) = x?i + xyj and r(t) = 2 costi + 2 sin tj, 0 st St. 4. Determine whether F(x,y) = xi + yj is a conservative vector field....
Q1. Evaluate the line integral f (x2 + y2)dx + 2xydy by two methods a) directly, b) using Green's Theorem, where C consists of the arc of the parabola y = x2 from (0,0) to (2,4) and the line segments from (2,4) to (0,4) and from (0,4) to (0,0). [Answer: 0] Q2. Use Green's Theorem to evaluate the line integral $. F. dr or the work done by the force field F(x, y) = (3y - 4x)i +(4x - y)j...
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.
For a vector field F(x)(2yarctanx)j find a function f such that F,y)-V/ h(2yarctanx)j find a function f such that F(x,y)-U For a vector field F(x,y)- 1+x2 and use this result to evaluate dr, where C: rit2, osis1
For a vector field F(x)(2yarctanx)j find a function f such that F,y)-V/ h(2yarctanx)j find a function f such that F(x,y)-U For a vector field F(x,y)- 1+x2 and use this result to evaluate dr, where C: rit2, osis1
5. Evaluate the surface integral SL.F 45, where F(x, y, z) = ri, and S is the part of the paraboloid z = Ty-plane, oriented upward. -x2 – y? +1 above the
1. Write f(z) in the form f(x) = u(x, y) +iv(x, y). (a) f(x) = 23+2+1 (b) f(3) = 2,270. Suppose f(z) = x2 - y2 - 2y +i (2x - 2xy), where z = x + iy, and express () in terms of .