Use Green's Theorem to determine the value of the following line integral 1 I - (7 x + 3 y ) dx + ( 9 x + 3 y )dy where C is the curve x2 + y2 = 4 traveled counterclockwise. Hint: don't forget to divide by N.

Q: ind the equation for the tangent plane to the surface z = In(6x2 +9y2 + 1) at the point (0,0, 0).…

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

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Q: Use Green's Theorem to evaluate the line integral ∫c ( x − y ) dx + ( x + y ) dy where C is the…

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Q: Use Stoke’s Theorem to evaluate the line integral ∮C(y+2z)dx +(x+2z)dy +(x+2y)dz, where C is the…

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Q: TYz dS; C:r= 2sent, y = t, z = -2cost.

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Q: Use Green's theorem to evaluate 2y3 dx – x³y2 dy, where C is the positively oriented circle of…

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Q: Evaluate the line integral fo(y+z) ds along the curve C defined by the straight-line segment 2 0, y…

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Q: Let C denote the oriented closed curve consisting of the line segment from (0, 0) to (V2, 0),…

A: Consider the provided question, (a) According to the given question draw a figure,

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

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Q: Can you show the steps on how to do this integral?

A: Consider the provided question, (3) Evaluate the integral by using the greens theorem,

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

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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: 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: Compute the line integral -xdy + ydx 2(x-y)2 + 4xy where L is the circle (1-x)2 + y? 3 with a…

A: We will find parametric equation of L and then convert whole equation in parametric form

Q: Evaluate the integral | (3x – 2 y + :)ds where C is the curve, C, and C, as shown. 3- y² + z² 2. 3…

A: Here, Curve C is equivalent to c1+c2. The point of intersections of c1 and c2 is at 0,1,0.

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

A: Cyclic integrals of the form Mdx + Ndy can be calculated using the Green s theorem.

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. p x2y dx,…

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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 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: Evaluate the line integral C:y² = 30x from (30,30) to (0,0). NOTE: Enter the exact answer. [-ydr +…

A: line integral

Q: Evaluate the integral [(3x – 2y + z)ds where C is the curve, C, and C, as shown. 3 y²+ z² 2 G 2* 3…

A: Given that ∫c3x-2y+zds. The objective is to find the integral value. ∫c3x-2y+zds=∫c13x-2y+z…

Q: • Use Green theorem to evaluate the Line integral $(x-3y) da +(42+y) dy whe re C, the Yectungle with…

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

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Q: Evaluate the integral ∫ x(y – 1)/z dz where C is a curve from z = 2 to z = –2 following a semicircle…

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Q: Evaluate the line integral ſe ry²ds, where C is three quarters of the circle a² +y? = 1, oriented…

A: C is the three quarters of the circle x2+y2=1, oriented counterclockwise. The parametric equation of…

Q: Evaluate the line integral - y)dz + (1+ } + æ*)dy, where C is the circle of radius 1 centered at the…

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Q: Use Green's theorem to evaluate $ 2y3 dx – x3y² dy, where C is the positively oriented circle of…

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Q: Use Green's Theorem to evaluate the line integr y? dx + x • when C is the circle of radius 2…

A: Introduction: Let C be a positively oriented, piecewise smooth, simple, closed curve, and D be the…

Q: The area of the surface obtained by rotating the curve y = -+ X°, 1sx< e about the line x = 24 is x3…

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Q: : The curve C is intersecting by 12r² +9y? = 36 cylinder and - V3r plane from the point (0, 2,0) to…

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Q: Evaluate the line integral f. y³ dx – x³dy, where C is the positively oriented circle of radius 2…

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Q: Evaluate the integral xy ds, where C is the curve consisting of the portion of the unit circle of…

A: The given integral is ∫Cxy ds where C is the curve consisting of the portion of the unit circle…

Q: Evaluate the line integral fx ds between (4,0) and (0,4), where C is the circle of radius 4 centred…

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Q: Evaluate the line integral (x – y°)dæ + (1+ y +z*)dy, where C is the circle of radius 2 centered at…

A: Hint: By green's theorem in a plane  If fx,y,gx,y be continuous in a region E of xy-plane bounded by…

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

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

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Q: State the Green’s theorem, then use it to evaluate the following line integral along the given…

A: Use green theorem

Q: Evaluate the line integral § (x − y) dx + (x + y) dy, where C is the circle with center the origin…

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Q: Use Green’s theorem to evaluate the line integral 2x2y dx + 6x3 dy, where C is the circle x2+y2 = 4,…

A: The answer is as follows:

Q: #3. Evaluate the line integral O (y dx- x dy) where C is the positively oriented circle with center…

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Q: Evaluate the line integral 2xyz dx + x²z dy + x?y dz where C is an oriented simple curve connecting…

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

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

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Q: Evaluate the double integral. (8x – 6y) dA, D is bounded by the circle with center the origin and…

A: The given data is: ∫∫D8x-6ydA To evaluate the double integral.

Q: y = 2x C = ƏD D y = x?

A: We have to evaluate the integral ∫Cx-ydx+3x+tan-1ydy. Where C is the curve in the given figure.

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

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