Use Stokes' Theorem to find the line integral of F = (xy, yz, xz) around the boundary of the surface S given by z = 9 – x2 for 0 < x < 3 and -3 < y< 3, oriented upward. Sketch both S and its boundary C. line integral F. dř =

Q: evaluate the line integral along the curve C. Scv+z) d s, C is the straight-line segment x = 0, y =…

A: To Evaluate∫C(y+z)dswhere C is straight line segmentx=0  ----(i)y=3-t -----(ii)z=t…

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 4…

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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…

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

A: Explained below

Q: Evaluate the integral for y dx +z²dy + x²dz, where C is the triangular closed path joining the…

A: Stokes theorem:  Let C be a closed curve S be a surface enclosed by curve C. F is defined every…

Q: valuate the line integral, where C is the given curve. z2 dx + x2 dy + y2 dz, C is the line segment…

A: Follow next step

Q: Use a double integral and Green's Theorem to find $C(x-y)dx+xydy,ke ( - ) dz + ry dy where C C is…

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

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Q: Use Green's Theorem to evaluate the line integral along the given positive (* 2x²y?) dy -4x хе dx +…

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Q: Use STokes's Theorem to evaluate:- @ Line integral ) (K+Z)dx +Cx-y)dy+ x dz c is ellips de fined by…

A: We'll answer the first question. Since the exact one hasn't specified. Please re-submit the question…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 5y +…

A: Use Green Theorem to evaluate  ∫C5y+9exdx+10x+7cosy2dy where, C is the boundary of the region…

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

A: Given integral ∮C3xydx+4xydy The objective is to evaluate the integral by using Green's theorem.

Q: 3- Use Stokes theorem to compute the line integral F . dr, where F = [e-3y, e, e201 and C is the…

A: By using the stokes theorem we need to find ∫CF·dr, where F=e-3y, ez, e-2x and C is the boundary of…

Q: Evaluate the surface integral. Approximate to three decimal places. I. 3y – x dS, S:r(u, v)=cos u i+…

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Q: Use Stokes' Theorem to find the line integral [((x² + x + 2y²)i + (y + z³)j + (z + 2x²)k) · dr where…

A: To Evaluate: The integral ∫C(x+2y2)i+(y+z2)j+(z+2x2)k·dr. where C is the boundary of the triangle T…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. xe-4*…

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Q: Use Stoke's theorem to calculate the surface integral || F. dS, where S F(x,y. =) = (* siny)i+ (e*…

A: Consider the provide question,

Q: Evaluate the integral for y*dx + z²dy + x²dz, where C is the triangular closed path joining the…

A: To evaluate the integral ∫Cy2dx+z2dy+x2dz where C is the triangular closed path joining the points…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 5y +…

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Q: use Green 's Theorem to evaluate the line integral. Orient the curve counterclockwise unless…

A: Solution Given  ∮C y2 dx + x2 dy, where C is the boundary of the square that is given by 0 ≤ x ≤ 1,…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. (3y +…

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Q: Evaluate the integral for Sy dx + z?dy + x²dz, where C is the triangular closed path joining the…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 5…

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Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | (3y +…

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Q: Use Green’s Theorem to evaluate the line integral along the given positively orientedcurve. Intrgral…

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

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Q: The area of the surface obtained by revolving the curve y = x² , for 1<x<2 , about the y- axis, is…

A: we will select a disc inside of thickness dy and radius xy will vary from 1 to 4circumferene of the…

Q: Evaluate the line integral F. dr where F(x, y, z) = x²y i+ x³ j+e² tan-¹ z k and C is the curve of…

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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: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | 8y dx…

A: Green's Theorem:- To find the line integral of a function along a closed curve C…

Q: Evaluate the line integral in Stokes' Theorem to find the surface integral [[ (V × F) · ndS, where…

A: Given: The vector is Fx,y,z=4y,-xz,exyz. To find: The value of∬S∇×F·ndS by using the line integral…

Q: Use Green's theorem to evaluate the given line integral around the indicated closed curve C. Then…

A: To evaluate: ∮C(y2dx+8xy2dy) Green's theorem says: ∮C(Pdx+Qdy)=∫∫∂Q∂x-∂P∂ydA

Q: Using Green's theorem, calculate the desired line integral on the plane for Sc [(m + n)x²y – y²]dx+…

A: Let, I=∮m+nx2y-y2dx+x2+m-nydy Where C is the closed curve of the area bounded by the curve y=x2 and…

Q: Use Stokes’ Theorem to evaluate the line integral  ∮  F·d r where F = 〈x^2−z^2, y, 2xz〉, and C is…

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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: Use Green's theorem to evaluate the line integral I of the one-form W = + æ sin? (y)) dæ + (x²…

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Q: Evaluate the integral for y dx + z²dy + x*dz, where C is the triangular closed path joining the…

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Q: Use Green fheorem to evaluate the line integral along the given positiv ly oriented curve. Sely +…

A: Given that the line integral is ∫Cy+exdx+2x+cosy2dy

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 integral of the function f(x,y,z) = y, where S is the surface z = x + y? with 0< x < 1…

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Q: Is Green's theorem applicable for all types of line integrals? Explain clearly. Use Green's theorem…

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

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. [(y+e*…

A: Green's theorem

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

A: In the given question we have to choose the correct options from the given options. we have to…

Q: Set up an integral that represents the area of the surface obtained by rotating the curve = e2t, y =…

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Q: Set up but do not evaluate the integral used to find the area of the surface generated by revolving…

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

A: 7/3 units

Q: Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve…

A: Consider the provided information, Given curve and interval, y=xe-x,2≤x≤4. Set up the integral of…