4. Let C be the circle |z| = 2 traversed once in the positive sense (counter clockwise). Compute : . Cos 3z dz (z-1)2 (z-3) (2.5

Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <: sos

A: See the attachment

Q: 2.2 Prove that Te -dz < 3 ez z2 +7+1 where C is the arc of the circle |2| = 3 from z = 3i to z = -3.

A:

Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <- 4

A:

Q: Let C' be the circle |2| = 3 in positive sense. Find ( sin(r2*) + cos(72²) dz cos(T2²) (2 – 1)(2 +…

A:

Q: Find the exact length of the curve. y= In{1 – x²), o s 1. 0 sxs! 7. I Ju =

A: We will find the exact length of the curve as shown below

Q: If C'is the circle of radius 3 centered at the origin, starting at the point (3,0) and moving around…

A: Answer and explanation is given below..

Q: 4. Let C denote the circle |z – 2i| = 1, taken in the usual counterclockwise orientation. Compute by…

A: Given: Let C  denote the circle z-2i=1 z-2i=1x+iy-2i=1x+iy-2=1 So, Centre of circle will be 0,2 and…

Q: 6. Evaluate [(x + y²)dx – xdy where C is the circle "x²+y² : = 1" with a counter- clockwise…

A:

Q: 4. Let C be the circle |z| = 2 traversed once in the positive sense (counter clockwise). Compute :…

A:

Q: 2.2 Prove that e? dz] < 3 +++1 where C is the arc of the circle |2| = 3 from z = 3i to z = -3.

A:

Q: 4. Let C be the circle [z| = 4 traversed once in the positive sense %3D sin 3z (counter clockwise).…

A:

Q: 2: Evaluate O (6y+x)dx+(y+2x)dy where C is the circle (x–2)²+(y-3)² = 4 | a) Using Green's Theorem

A:

Q: Express the circle specified by x = 2 cos(0) y = 1+ 2 sin(0) in Cartesian coordinates and find the…

A:

Q: 1. Use Green's Theorem to evaluate |F. dr, where F(r, y) = (3y- esin, 7x + Vy + 1) and C is the…

A:

Q: 13. Let C be the unit circle |z| = 1, described in the positive sense. Determine the %3D value of c…

A:

Q: 4. Evaluate y ds where C is the upper half of circle x² + y² = 9, traversed in the counterclockwise…

A:

Q: 3. a) Compute: f (Rez-32) dz where I is a directed line segment from z=0 to z=i. b) Let C be the…

A:

Q: zt e dz if t>0 and C is the circle z]=2. Evaluate 2ni C 2πίz+1

A:

Q: 12. Use Greens Theorem to calculate P y'dx -a'dy C where C consists of the arcs y=x² and y =x1/2,…

A:

Q: Scalar line integrals Evaluate the following line integral along the curve C.

A: Given:

Q: Find the areas of the regions Inside the lemniscate r2 = 6 cos 2θ and outside the circle r = √3

A: Given that: r2=6cos2θ,     r=3 To calculate the points of intersection,   Set the given equation…

Q: 2. In the figure to the right, FE is a tangent to circle O. D and F are connected so that EG = GF.…

A: Given from the figure

Q: Draw a sketch of the given arc C and evaluate S [(x² −2y)dx + (2x + y²)dy]. 2. C is the line segment…

A: Given integral: ∫Cx2-2ydx+2x+y2dy C is a line segment from  12,1 to 54,0 54,0 to 54,2   To find:…

Q: ) Let C be the arc from the point (3,0) to the point (0,3) on the circle x² + y² = 9. The value of…

A:

Q: Express the circle specified by x = 2 cos(0) y = 1+ 2 sin(0) in Cartesian coordinates and find the…

A:

Q: Exercise 1.2.16 Find the circle x2 +y² +ax+by+c=0 passing through the following points.

A:

Q: Find the length of the curve over the given interval. r = 2a cos θ, [−π /4, π/4]

A: Since, we have to find the length of the curve over the given intervalr=2a cosθ over the interval…

Q: 4. Let C be the circle |z| = 2 traversed once in the positive sense cos 3z (counter clockwise).…

A:

Q: 2.2 Prove that e zp- 3 where C is the arc of the circle |2| = 3 from z = 3i to z = -3.

A:

Q: Express the circle specified by x 2 cos(0) y = 1+ 2 sin(0) in Cartesian coordinates and find the…

A: Note: Equation of a circle with radius r and center at (h, k) is given by (x-h)^2 + (y-k)^2 = r^2

Q: 29. Let C be the quarter of the unit circle in the first quadrant, traversed coun- terclockwise from…

A: Explained below

Q: Express the circle specified by x = 2 cos(0) y = 1 + 2 sin(0) in Cartesian coordinates and find the…

A:

Q: 2.2 Prove that e zp- 3 2+z+1 where C is the arc of the circle |=| = 3 from z = 3i to z = -3. %3!

A:

Q: 5. Evaluate (y +tan x)dx+(x -2ry+y)dy, where C is the circler +y' =4 and is oriented in a positive…

A:

Q: Prove that e dz < ++1 3 where C is the arc of the circle |2| = 3 from z = 3i to z = -3.

A:

Q: 2. Use Green's theorem to evaluate fe e-x³ dx + (5x + sin(y²)) dy, where C is the circle x² + y² = 4…

A: Please see the below picture for detailed solution.

Q: z+i dz , where T is the circle Iz – 3i| = 1 traversed once (2) Compute counterclockwise.

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: Find the upper bound of |[∫c ez^2 + 1 / (z - 1)2 + 5] dz|, where C is the circle |z - 1| = 2.

A:

Q: Express the circle specified by r = 2 cos(0) y = 1+ 2 sin(0) in Cartesian coordinates and find the…

A:

Q: 10. (~Ch16 Review #17) Use Green's Theorem to evaluate | x?y dx – xy? dy where Cis ,2 the circle x2…

A:

Q: Express the circle specified by x = 2 cos(0) y = 1 + 2 sin(0) in Cartesian coordinates and find the…

A:

Q: dz b) C: z|= 4 is a circle calculate the integral .(z-1)(z² +9)

A:

Q: Let r(t)=(3t,4t -3,6t +1). Find the arc length traced by r(t) if 1st s7.

A: Given  rt=3t,4t-3,6t+1 To find the arc length traced by rt if 1≤t≤7 A vector valued function…

Q: Let G₁ be z = 6-√√36 - x² - y² and G2 be the upper nape of x² + y² - 3z² = 0. If S is the circle…

A:

Q: Let C be the curve connecting (1,1) to (-1,-1) clockwise around the circle x2 + y = 2 1 -dy + y? + 1…

A:

Q: Consider the given curve: R(f) = (2 cos f, 12f +3,-2 sin f) Reparametrize the curve using arclength…

A:

Q: 3 dz where C, is the top half of circle with radius (b) Compute the upper bound of 2,

A:

Q: Let C be the circle |z| = 4 traversed once in the positive sense (counter %3D clockwise). Compute :…

A:

Q: Express the circle specified by x = 2 cos(0) y =1+2 sin(0) in Cartesian coordinates and find the…

A: Solution