Evaluate the integral: I = S, dz where C is the circle |z|=1. O (A) I = –27ni. O (B) I = -3Ti. O (C) I = –5mi. O (D) I =-7ni. 2+1 2(2z+1) %3D %3D -

Q: given ∫∫s (x2z) dS and S is the part in z = sqrt(x2+y2), which lies in x2+y2 = 1 calculate the…

A: we have to evaluate ∬Sx2zdS Now, we have z=x2+y2 ⇒z2=x2+y2∂z∂x=xz and…

Q: Set up, but do not evaluate, an integral for the length of the curve. y = 6 cos x, Osxs 27 dx

A:

Q: Use Green's Theorem to evaluate the following line integral. Of dy -g dx, where (f,g) = (7x,11y) and…

A: Use Green's Theorem to evaluate the following line integral.

Q: Evaluate I = , dx dy where R is the region that lies inside the circle x2 + (y – 2)2= 4 and outside…

A: We have to find ∬Rdxdy where R is the region that lies inside the circle x2+y-22=4 and outside the…

Q: ) Evaluate the double integral I. y? dA, where R is the region that lies x2 + y? R between the…

A:

Q: Use Green's Theorem to evaluate the following line integral. i dy -g dx, where (f.g) = (7x,8y) and C…

A: We have,

Q: t C be the circle of radius 4 from 0 to pi/2.  What is the integral around C of  |z|2?   z=x+iy

A:

Q: find the area of the surface S: x² + y² + 2² = 4 -A <tan -^ (*) FO 6 < COS Cos FJ VI (2) 4 DEX TI 3…

A: The given Surface is                    x2+y2+z2=4 ........1where π6≤tan-1yx≤π3 and π4≤cos-1z2≤3π4…

Q: Evaluate the line integral C: y² = 27x from (27, 27) to (0,0). NOTE: Enter the exact answer. 6-₂…

A:

Q: Evaluate the integral f (1 – y³)dx + (x³ + ev²)dy, where C is the boundary of the region between the…

A: option (d) is correct

Q: Evaluate the integral / sin (9x? + 4y?)dA, where R is the region in the first quadrant R bounded by…

A:

Q: Evaluate the integral dz, le z+2 where C is semi-circle, C(t) 2e", te [0, 7].

A: According to the given information, it is required to evaluate the integral over C.

Q: evaluate the integrals around the circle Iz| = 2, counterclockwise. 9) 1 = dz, Find |I| 4z2+9 z+1 8)…

A:

Q: Evaluate the integral ∫C xy2ds, where C is the part of the unit circle x2+y2=4 in the first…

A: Use parametric to solve this

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 5…

A:

Q: Evaluate the line integral L(r – y*)dx + (1+ y² + =*)dy, where Cis the circle of radius 2 centered…

A: We have to evaluate the value of the integral

Q: x dy - y dx

A:

Q: Evaluate the integral 9y-x-3x-dz, where Cis the straight line from z = O to z = 1+ i. A 14 B. -14 ©…

A:

Q: Use polar coordinates to find the integral 16 - x² - y? dx dy where R is the circle x? + y? < 4.

A:

Q: Evaluate the integral (xy + xy²) dx + (2x² + x²y) dy over the curve C, defined by going in a…

A:

Q: Set up, but do not evaluate, an integral for the length of the curve. y = xe, osxS 8 dx Jo

A:

Q: Evaluate the line integral, where C is the given curve. Sc xy² ds, C is the right half of the circle…

A: Use parametric  method to solve

Q: Evaluate the line integral, where C is the given curve. xy ds, C is the right half of the circle x2…

A: C is the right half of the circle x2+y2=16 thus the parameterization of the circle is x=4cos t and…

Q: 3. Evaluate the integral: I = J dz where C is the circle |z|=1. O (A) I O (B) I =-3i. O (C) I =…

A:

Q: Evaluate y*dx – a*dy, where C is the boundary of the region between the circles a? + y² = 16 and %3D…

A:

Q: Evaluate the integral į. I. (1 - x - x² – y²)dA Where R is one-unit circle on the xy-plane.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A:

Q: Use Green's Theorem to evaluate the integral (x² – y)dx + 4.xdy where C is the circle x? + y? = 25…

A:

Q: 2. Use the appropriate integral theorem (and state which one you are using) to evaluate Lr*y dr –…

A:

Q: Consider the inetgral (11z + 2) dA where Ris the region between the circles z? + y? = 9 and z2 + y?…

A: Since R is the region between the circles x2+y2=9 and x2+y2=100. Therefore, we describes the region…

Q: Evaluate the line integral, where C is the given curve. | xy? ds, C is the right half of the circle…

A:

Q: Evaluate the integral i. (1 – x2 – y?)dA - Where R is one-unit circle on the xy-plane.

A: Note:- These are multiple questions and according to our company law i can do maximum one question.…

Q: Q3. a) Evaluate the following integral: (5x2 + 2y) dA where R is the region in the upper half-plane…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Evaluate the line integral L(a - )da + (1 + y° + æ")dy, where Cis the circle of radius 2 centered at…

A: We have to evaluate the integral.

Q: Find the exact area of the surface. :=+2y,0sxS1,0sys2 Oa 2+ n(4) Ob. Sin(3) 4. Oc3-In(5) Od 5…

A:

Q: What is the area of the region that lies inside the circle r + y y? = 5x? ² ? %3D 10.r and outside…

A:

Q: Use Green's Theorem to evaluate the following line integral. Of dy-g dx, where (f,g) = (8x,5y) and C…

A:

Q: B9. (a) Use the Cauchy integral formula to find zdz (z + 1)(22² + 3z –- 2) | where I is the circle…

A:

Q: dz ; C is a circle Iz-1| = 1/2 z4-1 z2

A:

Q: Evaluate the double integral y? -dA, where R is the region that x2 + y? R lies between the circles…

A:

Q: Use Green's Theorem to evaluate the following line integral. Of dy -g dx, where (f.g) = (7x²,8y?)…

A:

Q: Compute the double integral // Vx² + y² dA where D is the part of the first quadrant lying between…

A:

Q: Evaluate the line integral (y dr+yrdy) taken in clockwise sense along the hexagon whose vertices are…

A:

Q: (2x.y? -4y)ds

A:

Q: What is the value of the double integral 128(e – 1) e(42+8y)? dA, 2 R where Ris the triangular…

A:

Q: Evaluate the double integral Answer: dA, where R is the region that lies between the circles x² + y²…

A: Explanation of the answer is as follows

Q: I = Examine the given integral dz ;C z-i -|= 2 the circle

A:

Q: Use Green's Theorem to evaluate the following line integral. i dy -g dx, where (f.g) = (7x,8y) and C…

A:

Q: (c) (i) By using polar coordinate, evaluate ff, x2 + y² dA, if R is the region in between circle x?…

A: image is attached with solution.

Q: Given the area bounded by the parabola x– 4x + 12y - 20 = 0, the x-axis and the lines x = 1 and x =…

A: ∫ (y^2)dx is the formula for moment of inertia