|Use Green's Theorem to evaluate | -x'ydx+xy°dy where C is the boundary of the C circle x + y =16 traversed in a counterclockwise manner. %3D

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

A: Just I have used the Green's theorem to change the line integral into double integral and then by…

Q: Let C be the boundary of the portion of the plane x+y+z=2 that lies in the first octant, oriented…

A: It is a 3D and we have to draw in a sheet which is 2D. I is a tough task but I will try to draw it…

Q: Evaluate ſf, (3x + 4y²) dA where R is the region in the upper half - plane bounded by the circles x²…

A: As the areas are circular thus convert the integral into polar form. Now determine the limits of the…

Q: The tangent plane to the graph of the surface z=In(x2+y?) at the point (1,0,0) contains point…

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Q: Verify: Green's theorem in the plane for f(2x-y³) dx-xydy, where C is the boundary of the region…

A: Given information ∫c2x-y3dx-xydy Here, C is the boundary of the region enclosed by the circle…

Q: Let F = (5e**+1 + y)ï + (2x – sin(3y – 2))j and C be the boundaries of the circle x? + (y – 2)² = 4…

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Q: c) By using Green's theorem, evaluate $ (In (x²) + xy² – y²) dx + (ev + x²y – 3xy) dy, where C is…

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Q: the surface z = &x + 4y th=

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Q: 7. Use Green's Theorem to evaluate the integral f x²y dx - xy²dy where C: is the circle x² + y² = 4…

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Q: use green's theorem to evaluate ∫c 5y^3dx-5x^3dy where C is the circle x^2+y^2=4 counterclockwise

A: Given: ∫c 5y^3dx-5x^3dy where C is the circle x^2+y^2=4

Q: Apply Stoke's theorem to calculate S. (x + y – 4)dx + (2x – z)dy + (y + z)dz, where C is the…

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Q: Evaluate yds where S is the surface = x + 2y?, 0 <a < 1, 0<y S 2

A: Consider the surface, z = x + 2y²

Q: a. Which of the following surface graphs represents f(x,y) = y²? OA.

A: Given, the surface                           z=f(x, y)=y2

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

A: Greens theorem states that "for closed curve C enclosed a region R then the line integral along the…

Q: Let C be the circle |2- i 2 oriented counterclockwise. Evaluate the following integral 1. z(2² + 4)

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

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Q: Suppose f(x, y) satisfies the basic existence and uniqueness theorem in some rectangular region Rof…

A: Consider the given: Let the function f(x,y) satisfies the basic existence and uniqueness theorem in…

Q: c) By using Green's theorem, evaluate (In (r) + ry – y²) dx + (e" +x²y - 3ry) dy, where C is the…

A: Green's therorem establishes relationship between double integral and line integral. Double integral…

Q: 17. Evaluate the integral: S, 9x? – 6dx. 18.Determine the center of the circle x² +y² = 25. %3D

A: (17)  Given that I=∫-159x2-6 dx It is known that ∫xndx=xn+1n+1 So, I=9x33-6x-15 =3x3-6x-15 Now we…

Q: 7) Verify Stoke's theorem when F= (2ry- a)î – (x² – y²)ĵ and C is the boundary of region enclosed by…

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Q: Verify Stoke's theorem for A=(2x-y)i-yz²j-y*zk where S is the upper half 5A. surface of the sphere *…

A: Consider the given vector and sphere equation. A→=2x−yi−yz2j−y2zk and x2+y2+z2=1 Since S is the…

Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

A: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is Then x…

Q: F. dr = 0 for every closed curve Cin R, an open connected region. %3D True O False

A: Explanation of the solution is given below.....

Q: Find the extreme values of the function ƒ(x, y, z) = xy + z2 on the circle in which the plane y - x…

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Q: Find the area of the band cut from the paraboloid x² + y² – z = 0 by the planes z = 2 and z = 6.…

A: Given equation is, x2+y2 = z Band cut from the given paraboloid by the planes z = 2; z = 6 Area of…

Q: 10. Using Stoke's theorem, evaluate y dx+ xz dy+x² dz where C is the boundary of the triangle cut…

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Q: 9. Using Stoke's Theorem Evaluate [(2x – y)dx – yz dy – y zdz) where c is the circle x +y =1,…

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Q: (a) Let f(z) = %3D (z + 4- i) (z4 + 5z³) Using CRT, evaluate the integral Of(2)dz, where the contour…

A: In the given question we have to evaluate the integral                               where the…

Q: Use spheri\cal coordinatcs Evaluate y'zdV, where E lies above the cone 4 = /3 and below the Sphere…

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

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Q: Describe and sketch the surfaces in space (R') defined by the following equa- tions: (a) y = -z +1…

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Q: EVALUATE § 7. d² USING STOKE'S THEOREM 3xz^ + ex² ₁ + 2xy^ с F(x, y, z) = 3XZ1 te C IS THE CIRCLE…

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Q: The tangent plane to the graph of the surface z=In(x2+y?) at the point (1,0,0) contains point…

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Q: Given that o is the part of the surface z = 4 – x in

A: Given, the surface z = 4 - x in the first octant from y = 0  to  y = 2. If ψx, y, z=xyz, F(x, y, z)…

Q: B is the first quadrant part of the region enclosed by the circles x2 + y? = a? and x2 + y? = b2…

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Q: Let be s a surface compaund by the union of s, qnd Sz An expression to get the Area of the Surface…

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Q: Let YR be the circle of radius R with counter clockwise orientation. Prove that 1 -dz = 0. lim z3 +…

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Q: Q-3 If R is a closed bounded region in the xy-plane whose boundary curve is C with arc lengths and…

A: Given R is a closed bounded region in the XY plane whose boundary curve is C with arc length s  and…

Q: The tangent plane to the graph of the surface z=In(x<+y<) at the point (1,0,0) contains point…

A: and point (1,0,0)

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 y dx+3xy dy, where C is the boundary of the semiannual region D in the upper half-plane…

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

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Q: Find the polar eauation for Hhe curve Cartesianm eavation. represented by the given 2.

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Q: 49. Verify Green's theorem in the plane for $ (2x -y)dx – xy dy, where C is the boundary of the…

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Q: c) By using Green's theorem, evaluate (In (z²) + ry? – y²) dr + (c" + r*y-3ry) dy, where C is the…

A: We have to evaluate ∮Clnx2+xy2-y2dx+ey+x2y-3xydy where C is the region bounded by the circles…

Q: The tangent plane to the graph of the surface z=In(x2+y²) at the point (1,0,0) contains point…

A:

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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