6. Use Green's Theorem to evaluate the line integral fc 2xy dx + (x² + y²) dy, if C is the ellipse 4x2 + 9y? = 36.

Q: Use Green's Theorem to evaluate the line integral. cx2 - y?) dx + 5y? dy C: x² + y² = 9 (x² .

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Q: Evaluate the line integral y = x² from (-1, 1) to (1, 1) and the line segment from (1, 1) to (−1,…

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Q: Jse Green's theorem to evaluate line integral | V8 + x3 dx + 9xy dy where C is a triangle with…

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Q: evaluate both the line integral and the double integral. 16. P(x, y) = 2x – x³y°, Q(x, y) = x³y°, C…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. xy2 dx…

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Q: The double integral I S Vx2+ y dydx in polar coordintes is:

A: Given: To explain the correct option of the given statement as follows,

Q: 4. Use Green's Theorem to evaluate the line integral | 2xydx+ xy'dy, where C is the triangle with…

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Q: Use Green's Theorem to compute the line integral | ry? dx – x² dy, -

A: Here we are going to use Greens theorem to find the line integral. Since, to compute the integral…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve.  xy2…

A: Our Aim is to evaluate the line integral along the given positively oriented curve xy2 dx+3x2y dy…

Q: 2. Use Green's theorem in order to compute the line integral P (x – 4)³ dy – y³ dx where is the…

A: We need to compute the given integral using Green's theorem . ∮C(x-4)3dy-y3dx Where is the circle of…

Q: Calculate the double integral (x + y)²ex* - y² dx dy where R is the square with vertices (2, 0), (0,…

A: According to the given information, it is required to find the integral over R where R is square.

Q: Evaluate the line integral xyld x + (x²+y)dy] +. where c is the saruare farmed by the lines

A: Let us consider a line integral ∫CP dx+Qdy then it can be written as  ∫D∫∂Q∂x-∂P∂y dA  Where, P and…

Q: Evaluate the line integral (direct method) | (3x– y) dx – x dy , where C consist of the parabola…

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Q: Solve the integral. + yz )do; o: part of the plane x + y +== 6 that lies in the first octanct.

A: Solution:

Q: Use Green's Theorem to evaluate the line integral S(x² + y²)dx + (x² – y²) dy where C is the…

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Q: Use Green's Theorem to evaluate the line integral Jo (y - x)dx + (2x - y)dy for the given path. C: x…

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Q: Evaluate the triple integral. 7x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: Here, E is the surface boiunded by the  paraboloid x=5y2+5z2 and the plane x=5. Now, at x=5,…

Q: Evaluate the line integral (direct method) |(3x– y) dx – x dy , where C consist of the parabola y=…

A: Given integral is, ∫C(3x-y)dx-xdy

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. xy2 dx…

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Q: Use Green's theorem in order to compute the line integral (2sin z + 3y²) dx + (sin(4®) + 2x³) dy…

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Q: Describe the bifurcation for the following dy - Ay - y %3D dt

A: The saddle node-bifurcation: Let y˙=f(α,t) is the system of equation, the to find the saddle-node…

Q: Use either form of Green's Theorem to evaluate the following line integral. $9x²1² 6 C $9x³y² dx +…

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Q: Evaluate the unoriented line integral (2æ² + y² + z²) ds along the parametric curve a : [0, 1] → R³…

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Q: 4. Use Green's Theorem to evaluate the line integral | 2xydx+ xy*dy, where C is the triangle with…

A: The given triangle C with the vertices (0,0),(1,0) and (1,2) is as as shown below.

Q: Evaluate the line integral Jo 9x²yzds with respect to s along the с 2 curve C: x=t, y = t², z = /t³…

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Q: 5) Evaluate the line integral S YX²dX + XY²dY on curve C, where C is the upper portion of the www m…

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Q: Use the Green's Theorem to evaluate the line integral 2xydx + x² – y² dy where C is the curve…

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Q: Use Green's Theorem to evaluate the line integral. y dx + 7x dy C: square with vertices (0, 0), (0,…

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Q: Evaluate the triple integral. SSLĘ 8x dV x = 2y2 + 2z2 and the plane x = 2. where E is bounded by…

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Q: 2/ Find the line integrals of the ellipse+3= ellipse by x = acos(t) ,y= bsin(t) 1 , parameterize the…

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Q: Use Green's Theorem to evaluate the line integral |(y - x)dx + (2x - y)dy Ic

A: Put the value of x and y and then simple integration.

Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | 6y3…

A: given circle x2+y2=4

Q: 8. Verify Green's Theorem for (6y – 3y? +x) dx + yx*dy where C is shown below by (a) computing the…

A: Given integral is ∮C6y-3y2+xdx+yx3dy Here C consists of two line,  C1:Line joining 0,0 and…

Q: Compute the integral |(5y + pz2020, ) dx + (19x – e-4ycos(v) sin y) dy over the portion of the…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 7y dx –…

A: To evaluate the integral ∫C7y3dx-7x3dy, identify the values of P, Q, then find its partial…

Q: C3x-3y2 +2x2) dxt (3y-3x2+2²)dy (3²-3xytx*2yz)da calculate the curvilinear integral.where cis any…

A: Let's find.

Q: Evaluate the triple integral III xy dV where E is the solid tetrahedon with vertices (0, 0, 0),…

A: The given integral is, ∫∫∫E xydV Here E is the solid tetrahedron with vertices O0,0,0, A10,0,0,…

Q: Evaluate the triple integral. 4x dV, where E is bounded by the paraboloid x = 7y2 + 7z² and the…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 7. Use Green's Theorem to compute the line integral | ry? dx – x² dy, where C is the triangle with…

A: ∫xy2dx - x2dy triangle vertices are (0,0), (2,0), and (2,2)

Q: 2. Compute the scalar line integral xy ds where C is the part of the circle of radius 2, centered at…

A: Put x=2cost , y=2sint

Q: # 4. Use Green's Theorem to evaluate the line integral P (y*dx +2xy° dy), where C is the positively…

A: Given integral is, ∮Cy4dx+2xy3dy

Q: Use Green's theorem to evaluate the closed line integral: . x²y dx +x'y dy along C between -1 < x< 2…

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Q: Use Green's Theorem to evaluate the line integral (у — х) dx + (2х — у) dy for the given path. C:…

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Q: Evaluate the line integral: f y² dx + x² dy by parameterizing C where the curve C is a square R with…

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

Q: Verify Green's Theorem by using a computer algebra system to evaluate both the line integral and the…

A: According to question, F = P i + Q j,   P(x, y) = 2x,   Q (x, y) = x3y6 .

Q: Evaluate the triple integral. 8x dV, where E is bounded by the paraboloid x = 7y2 + 7z2 and the…

A: here, E is bounded by the paraboloid  x=7y2+7z2  and the plane x=7.    so , at    x=7 ,     y2+ z2…

Q: Use Green's Theorem to evaluate the line integral , 6y² dx + 5x² dy, where Cis the boundary of the…

A: Green's Theorem: ∮C(Pdx+Qdy)=∫∫R∂Q∂x-∂P∂ydA

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 2y3 dx…

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Q: Use Green's Theorem to evaluate the line integral along the gi | 4y3 dx - 4x³ dy Cis the circle x2 +…

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Q: 1. Evaluate the line integral I = = [v¢4x° + y*) dx + x(2x° + 3y*) dy] around the ellipse x/a? +…

A: The given line integral is, I=∮y4x2+y2dx+x2x2+3y2dy We know the Green's theorem:…