.† Use Stokes' theorem to show that Sc(y+2)dx+ (z +x)dy+ (x+y)dz = 0, where C is the curve of intersection of the cylinder x2 + u? = 2u and the plane y = z. %3D

Q: Let F = %3| Use Stokes' Theorem to evaluate curlF · dS , where S is the hemisphere x? + y? + z² =…

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Q: 4. Use Stokes’ theorem to evaluate fa F. dr, where F(x,y, z) = (xy,yz, zx), and C is the triangle…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Let F Use Stokes' Theorem to evaluate F · dī, where C is the curve of intersection of the parabolic…

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Q: Verify Stokes' theorem for F = (x+y-4) i+3xy j+ )k, over the surface of the hemisphere x2 + y2 + z2…

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Q: Which of the following is the surface area of the surface generated by revolving the curve y = in…

A: We have to find

Q: Which of the following is the surface area of the surface generated by revolving the curve y = in…

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Q: I = y dx + (z — х) dy — ydz, Jc

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Q: Find the area under the parametric curve x=t(1+t) , y=1/(1+t) ,  between t= [0,1]

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Q: Determine which of the following gives the area of the surface obtained by revolving the curve y =…

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Q: 3.) Verify the conclusion of Stokes' Theorem given F(x,y,z)=(x-y,y-z,z–x) where S is the surface cut…

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Q: Q2) Evaluate each side of Stokes theorem for a portion of cylinder : p=2m 0<¢<a /3, 1<z<2 Н-Iz /2пр…

A: according to stokes theroem closed linr integral of H is same as the surface integral of curl of H.…

Q: Use Stokes' Theorem to compute 1 z? dx + (ry) dy + 2020 dz, where C is the triangle with vertices at…

A: Given I=∮C12x2+xydy+2020dz where C is the triangle with vertices at 1,0,0 , 0,2,0 , 0,0,2 traversed…

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: Compute the volume of the solid below 2 – a? – y? and above the region D in the xy-plane. The…

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Q: Use Stokes' Theorem to find the line integral [((x² + 2y² ((x + 2y²)i + (y + 2²)j + (2 + 2x²)k) · dř…

A: Given that C is boundary of triangle with vertices 1,0,0,0,1,0,0,0,1 So, equation of the plane with…

Q: Use Stokes' theorem to evaluate      CF · dr  where C is oriented counterclockwise as viewed from…

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Q: / Use Stokes theorem to evea luarte the SS Canl F.n ds, S being that Part of the Sar face of the…

A: Solution::

Q: CurlF dS x+y' +z =9, z20 se Stokes' Theorem to compute s for the hemisphere intersected with the xy-…

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Q: Find an integral for the area of the surface generated by revolving the parametric curve about the…

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Q: e of the solid E whose boundaries are given in rectangular located inside the circular cone x? + y?…

A: In this question we will use basic of calculus i.e volume of cone. We will simply draw the given…

Q: 3. Consider A(r) = (y, -x,0), and the line integral A• dr along the C boundary of the plane x + y +…

A: The given vector function is A(r)=(y,-x,0)., the line integral ∮CA·dr is along the boundary of the…

Q: Use Stokes' theorem to evaluate      CF · dr  where C is oriented counterclockwise as viewed from…

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Q: 5 + 2? + y, the cylinder Evaluate e dV where E is enclosed by the paraboloid z = E 2 + y? = 1, and…

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Q: Question 7 ( Let C be the curve of intersection of the cylinder x2 + (y - 1)2 = 1 with the plane y =…

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Q: Use Stokes' Theorem to calculate rot F dS, where F = ri + yj + rk and S is the surface given by the…

A: This is a problem of vector calculus. By using stokes theorem formula we will evaluate given…

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

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Q: 1. Compute ff,(V × F) - dS, where S is given by r² + y? + (z – 1)? = 2 and z > 0, and F(x, y, z) =…

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Q: 2. Find the area of the surface generated by revolving the given curve about the y -axis. (a)…

A: The surface area of the curve is given by

Q: Use Stokes' Theorem to evaluate L* + cos x) dx + (sin y + z²) dy + x dz where C is the closed curve…

A: To Evaluate: Use Stoke's Theorem:

Q: - Prove Stokes' Theorem by verifying it for F= [y,z,x] and S the paraboloid. %3D te CEY2=(x, y) = 1…

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Q: The area of the surface obtained by revolving the curve Vy+1 for a-1.) 2л. dy 4y +4 a b. TV4Y +5 dy…

A: Area of surface revolving around y axis is  given below.

Q: curl F dS, where Use Stokes' Theorem to determine which of the following is equivalent to F(x, y, z)…

A: The given function is F(x, y, z) = 2x2 i^ + xy j^ + ez k^.The surface S is the part of the…

Q: 3. Suppose F z = 4 – a? – y? above the r- y plane, oriented upward. Calculate fe F dĩ in two ways:…

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Q: Use Stokes’ theorem to evaluate the line integral

A: Stokes’ theorem

Q: Which of the following is the surface area of the surface generated by revolving the curve y = in…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Which of the following represents the are a of the surface of the portion of the cylinde 2+ z? = 4…

A: We need to find the integral which represents the area of the given surface. This can be done as…

Q: Determine which of the following gives the area of the surface obtained by revolving the curve y =…

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Q: Let F(x.y.z)=-y²i +xj+z? k, S is the shaded part in the figure at right and C the boundary curve of…

A: We will find out the required value.

Q: 1. Use Stokes' Theorem to evaluate curlF.dS where F =z'i+ (4y-y) j+2zk and S is the portion of z = r…

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Q: The curve a- y = e+ tanh y, a, y ER is given parametrically by Select one: O x(t) = t, y(t) = t + e'…

A: Parameterized the  curve which is given here

Q: 2. Use Stokes' Theorem to evaluate curlF.dS whereF = 2y i + 3z j+(z – z) k and S is the portion of y…

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Q: State the Stokes' Theorem. Ise the Stokes' Theorem as stated in (a) to evaluate the lin |F- dř here:…

A: We have to write the stokes theorem and using it We have to find the given line integral according…

Q: How many points are there on the surface z = dx +y such that the tangent plane to the surface is…

A: Given :  d=maxa,b,c⇒d=max2,1,0⇒d=2 So,z=dx2+y2⇒z=2x2+y2 Also, dx+y+z=0⇒2x+y+z=0 Let fx,…

Q: 2. Use Stokes' Theorem to evaluate ſ. V × F·n dS where F(x, y, z) = and C is the part of the sphere…

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Q: Use Stokes' Theorem to evaluate , (x + y )dx + (2x – 3)dy + (y + z)dz over the boundary of the…

A: First we will learn about Stokes theorem little bit. If "F1 i + F2 j + F3 k" is a differentiable…

Q: Define stokes theorem and evaluate the line integral SF.r'(s) ds where F = [4z, 2x, 2x], C: the…

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Q: Use Stokes' Theorem to find the line integral (x+ 2y°)ï+ (y + z²)j+ (z + 2r²)k) · dř where C is the…

A: To find the line integral, Using stokes theorem.

Q: Use Stokes' Theorem to evaluate |/. CurlF dS, where F(r, y, 2) = xyzi + xj + e" cos zk and S is the…

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Q: Use Stokes' Theorem to evaluate: L 20wy°zdar + 20°yzdy + (z°y? – 2)dz Where C is the curve given by…

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Q: 'Use Stokes' Theorem to compute | 1 F. dr where C is the curve where the cylinder a? + y? = 1…

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