_y²x I+ y? vertices (0, 0), (1,0), (1, 1), and (0, 1). 1. tan- y dx - dy, where C is the square with

Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. ye* dx…

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Q: 50.) Show how to use a line integral to find the area of a circular disk of radius r

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Q: Use Green's Theorem to evaluate the line integral . curve C: the boundary of the region bounded by…

A: Given that ∮Cex2dx+siny−7x2dy, where C is the region bounded by the parabola  y=x2 and x=y2. By…

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Q: Use Green’s Theorem to evaluate  ∫ sin 5y dx + 5x dy  around the boundary curve C of the region R,…

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

A: To evaluate the below line integral. ∮C5y2dx+3x2dy

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. 2x + 3y dx + e…

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Q: Evaluate the line integral, where Cis the given space curve. xevz ds, C is the line segment from (0,…

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Q: Evaluate F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to…

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Q: let R be the area between the line y=x and curve y=3x-x2, calculate the integral in the picture.

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Q: Let F = (y.x) and C be the circle of radius 9 centered at the origin oriented counterclockwise.…

A: Given: F=y, xC is the circle of radius 9 centered at the origin.Therefore we parametrized the curve…

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

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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: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 3y3 dx…

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Q: Use Green's Theorem to calculate line integral o sin(x²) dx + (3x – y) dy where C is a right…

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Q: Use Green's theorem to determine the value of the integral where the curve x2 + 4 = 1 traveled…

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Q: Evaluate the line integral, where C is the given curve. xevz ds, C is the line segment from (0, 0,…

A: We have to evaluate the integral ∫Cxeyzds, where C is the line segment from 0,0,0 and 3,2,4. The…

Q: Use Green's theorem to find the line integral of 2x dx – 7x2 dy counterclockwise around the triangle…

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

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Q: Use Green's theorem to evaluate the line integral (F-ds where F = 2.xyi + (x- y')j and C is the path…

A: F→ = 2xy i⇀ + x-y2j⇀C is the path along the curve y = x3,From 0, 0 to 1, 1and x = y2 from 1,1 to 0,…

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

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve 5y³ dx -…

A: We know that , Green's theorem ,  Consider C be a positively oriented  , simple , closed , piecewise…

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

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Q: Set up the double integral in rectangular coordinates to compute the area of the surface z = x2 +…

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

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Q: Let R be the finite plane region trapped between the curves y = Vx and y =x². Sketch R and express…

A: Given R is the  region in between the curves, y=x and y=12x2. To plot the graph, consider the table…

Q: iii) Set up an integral for the area of the surface generated by rotating the curve about the…

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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: y*dx + x*dy = (N, – M,) • dA (м, - м,) ал

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

A: Line integral

Q: Evaluate the line integral $ x*dx + xydx where C is the triangle with vertices at (0, 0), (0, 6) and…

A: Given Line Integral is ∮x4dx+xydy , where C is a triangle with vertices at (0,0), (0,6) and (6,0)…

Q: Evaluate the line integral Vo• dr for the following function o and oriented curve C (a) using a…

A: The general form of the parametric equation of the curve in three-dimensional space is given by…

Q: Evaluate this integral Sc v – 2x)dy – (yx – x²)dx where C is a curve consisting of C, which is a…

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Use spherical coordinates to evaluate the integral •√₁-x² √√₁-x²-x² (x² + y² + ²)dzdydx.

A: To evaluate the integral using spherical co-ordinate system :-

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 integral. Assume that the curve Cis oriented counterclockwise. 2…

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

A: given circle x2+y2=4

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. L(y -…

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Q: image attached

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

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Q: Evaluate the line integral using the Fundamental Theorem of Line Integrals. (3y dx + 3x dy), where C…

A: Given line integral is: I=∫c3ydx+3xdy It can be rewritten as: I=3∫cydx+xdy                ....(1) As…

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

A: Using the Green's theorem.         ∫C  (M dx+N dy)=∫∫D ∂N∂x-∂M∂ydA.    ∴    ∫C y…

Q: Use Green's theorem to evaluate the line integral [F•dš where = 2xyi +(x- y')j and C is the path…

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

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Q: *Sketch all appropriate regions or solids." Evaluate the integral [[2y² cos(xy) dydx.

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

A: Green's Theorem: Let C be a simply connected piecewise smooth curve with a positive or counter…

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

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Q: Evaluate the line integrals using the Fundamental Theorem of Line Integrals: ∫c (yi+xj)*dr Where C…

A: Introduction: One method for extending this theorem into higher dimensions is the gradient theorem,…