Let C be the positively oriented circle x? + y? = 1. Use Green's Theorem to evaluate the line integral fa 19y dr + 20x dy.

Q: Find the integral surface of the linear PDE xp - yq = z which contains the circle x² + y? = 1, z=1.

A: From Lagrange method

Q: Evaluate, using Cauchy's integral formula: sin tz? + cos Tz? () dz where C is the circle |z| = 3 (z–…

A:

Q: Evaluate the line integral fc (2 + x*y)s, where C is the half circle x + y? = 1 in the upper half…

A:

Q: Use Green's Theorem to evaluate the integral o (3x - y)dx + 4xdy where C is the circle x +y? = 1…

A: Consider the given integral. ∮C3x2-ydx+4xdy Here C is the circle x2+y2=1 The Green's theorem can be…

Q: B) Use Green's Theorem to evaluate /F-dr, where C is the circle r² + y? = 4 and F (r, y) = (y – 2…

A:

Q: Let C be the positively oriented circle x2 +y2 =1. Use Green's Theorem to evaluate the line integral…

A: C is the circle  x2 + y2 = 1 The integral to find  ∫c3ydx +9xdy

Q: 4. Use Cauchy's theorem or integral formula to evaluate the integrals. sin z dz b. a.-dz, where C'…

A:

Q: Calculate the line integral ∫Cy2ds, where C is a part of the circle x=acost, y=asint, 0≤t≤π/2.

A:

Q: Use Green's Theorem to evaluate the line integral f(e*c - 2y)dx+(5x+ev* dy, where C is the 15. 2cos:…

A: We need to find integral.

Q: Use green's theorem to calculate the integral Fdr, F(r, y) = (e* + x²y , e³ – ry² + sen(3) + 2)…

A:

Q: The foilowing describes a para bolic path C: Pt) = (t, 2, 1-t?) %3D if F = (32, x + y+Z, 2x >,…

A: The given problem is to evaluate the line integral of the given vector field over the given…

Q: Use Cauchy's theorem or integral formula to evaluate the integrals. sin z dz T dz, where C is the…

A: Using Cauchy's theorem or integral formula we evaluate the given integrals.

Q: Let C denote the unit circle centered at the origin in C. Then r 1 ||1+ z+ z dz , 2ni ²l dz , where…

A:

Q: Use Green's Theorem to evaluate the integral (3x² – y)dx + 3xdy where C is the circle a? + y? = 1…

A: As we know from the Green's theorem; ∫CMdx+Ndy=∫∫D∂N∂x-∂M∂ydA   Given; I=∫C3x2-ydx+3xdy So, M=3x2-y…

Q: Let C be the unit circle oriented counterclockwise. A line integral that represents the area inside…

A: Use Greens theorem and Stokes theorem to solve the following question.

Q: Evaluate the integral: I = S, dz where C is the circle |z|=1. O (A) I = –27ni. O (B) I = -3Ti. O (C)…

A: By using Cauchy integral Formula-

Q: Use Green's Theorem to evaluate the integral (2x? – y)dx + 4xdy where C is the circle x? + y² = 9…

A: To evaluate the given integral using green's Theorem.

Q: Integrate counterclockwise around the circle |z – 6i| = 3. z(z – li)? - NOTE: Enter the exact…

A:

Q: Use Green's Theorem to evaluate the integral (x² - y)dax + 3xdy where C is the circle x² + y² = 1…

A:

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

A: Use parametric to solve

Q: Use Green's Theorem to determine the value of the following line integral 1 I - (7 x + 3 y ) dx + (…

A:

Q: Let C be the positively oriented circle x? + y? = 1. Use Green's Theorem to evaluate the line…

A: Given : C is a positively oriented circle x2+y2=1 We have to evaluate the line integral…

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. p x?y dx,…

A: green's theorem transforms the line integral around C into double integral over the region inside C…

Q: Let C denote the unit circle centered at the origin in C. 1 Then |1+ z + z 1 dz, 2ni where the…

A:

Q: Let C denote the unit circle centered at the origin in C. 1 Then |1 + z + z*l° dz, 2πί C where the…

A: Introduction: A complex number has a conjugate. The conjugate of a complex number is determined by…

Q: Use Cauchy's Integral Theorem to evaluate fr 12z-3(2-42 dz where I' is the circle |z| = 2 described…

A: Given ∫ez2z−3z−42dzWe know the formula ∫fzz−an=2πin−1!fn−1aWhere 'a' is pole of order nGiven region…

Q: Use Stoke 's Theorem to evaluate [ V. dr, where v= y²i + xyj + xzk, and c is the bounding curve of…

A:

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 line integral a ds where C is the unit circle, æ? + y² = 1, oriented in the…

A:

Q: Find the integral fc ez dz where C is the circle |z| = 3 in CCD. (z – 1)2(z – 2) %3D -

A:

Q: ⒸFind S (x- y²) dA, where I is bounded by the circle of D center (0,0) and radius 2.

A: As per as our guidelines i am supposed to answer

Q: Let C be the circle x + y = 16 oriented counterclockwise. %3D Use Green's Theorem to evaluate the…

A: Let C be the circle x2+y2=16 oriented counterclockwise. Use Green's theorem to evaluate the…

Q: Let C denote the unit circle centered at the origin in C. 1 ||1+ z + z ||1+z+ z? dz , 2ni Then where…

A:

Q: 15. Evaluate the contour integral e3z I (z+ 2)ªdz where C' is the circle |z| = . 9e6 2 O 27 9e-6 O…

A:

Q: Evaluate the line integral |(2? + y) dx – x dy where C is the line segment from (2,5) to (5,9) in…

A:

Q: Evaluate ffp(4xy + 1) dA, where R is the region in the upper half-plane bounded by the circles a? +…

A:

Q: Let C denote the unit circle centered at the origin in C. 1 1+ z +z*° dz, dz , Then 2ni where the…

A:

Q: Evaluate the line integral G. dr with G(x, y) = xyi+ 2y² j, and C is the closed path comprising the…

A:

Q: Evaluate the line integral ſc(4y+ tan? x)dx + (6x – evsin´y)dy over curve C that is the circle x2 +…

A: Green's theorem problem....

Q: Compute the line integral f, x?dx + y²dy where the path C consists of the arc of the circle x? + y?…

A: Here we solve the given problem of integral.

Q: Compute the line integral Sy?a dl where y is the part of the circle centered at the origin and of…

A:

Q: Evaluate the contour integral and use appropriate graphs to illustr where is the circle with…

A: Given : ∮e2021zz2+1z2-1dz To Find : (a) z-i =1                                                     b…

Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…

A: Greens theorem

Q: Let C be the unit circle {z : |z| = 1} with positive orientation. By any method, compute the…

A:

Q: Using Green's Theorem, evaluate the line integral |(-*y)dr + ay*dy re C is the circle a2 + y? = 1…

A: Let C is a counterclockwise oriented simple closed curve with the interior region R. According to…

Q: 3. (a) Use Green's theorem to evaluate the line integral 4 y* dx – a* dy where C is the positively…

A:

Q: the line integral SexY² ds where C is the of the Circle x² + y²=4 oriented clockwise Evaluate Cight…

A:

Q: Let C be the positively oriented circle x2 +y2 =1. Use Green's Theorem to evaluate the line integral…

A: The given circle C is  x2 + y2 = 1 Heree the centre of the circle is (0, 0) Radius of the circle r =…

Q: Using Green’s formula, evaluate the line integral ∮C(x−y)dx+ (x+y)dy, where C is the circle…

A:

Q: Evaluate the line integral: x dy – y da x² + y² where C is the circle x² + y? = a², a > 0, oriented…

A: