Use Stokes' Theorem to find the line integral of F = 3yi + 2zj + 5xk around the triangle obtained by tracing out the path (3,0, 0) to (3, 0, 4), to (3, 5, 4) back to (3,0, 0). line integral = F dr =

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

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Q: Let F = 8(x + y) i +3 sin(y) j. Find the line integral of F around the perimeter of the rectangle…

A: Proceed as shown...

Q: Let F = 4(x + y) i + 6 sin(y) j. Find the line integral of F around the perimeter of the rectangle…

A: Let F = 4(x + y) i + 6sin(y) . Find the line integral of F around the perimeter of the rectangle…

Q: Evaluate the line integral using the Fundamental Theorem of Line Integrals. Use a comp cos(x) sin(y)…

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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: Show that the line integral is independent of path, and use the Fundamental Theorem for line…

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

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

A: To evaluate the given line integral along the given positively oriented curve. ∫Cyexdx+2exdy Where C…

Q: 3 Let S be a square plate with boundary C having length of each side as 2 units and lying in the…

A: The plane is given as y = 1, so plane S is y = 1   The unit normal vector to the surface S is:

Q: Compute the moments of the semicircle x2 + y2 = R2, y ≥ 0 as line integrals. Verify that the…

A: Given semicircle x2+y2=R2,  y≥0 The figure of this semicircle is shown below. In the above figure,…

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

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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: Caluulate the friple integral using curvilinear coordina tes : t is the region between 1|- 2x²- 2y²…

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Q: Calculate the line integral fe F. dr, where F = (ry, x² + y² + z², yz), and C is the boundary of the…

A: Given F→=xy,x2+y2+z2,yz and C is the boundary of the parallelogram with vertices…

Q: IntegrateF(x, y, z) = z, over the portion of the plane x + y + z = 4 that lies above the square…

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Q: Convert dzdydx /9-x-y Into an integral of cylindrical coordinates

A: Given∫03∫09-x2∫3--x2-y2x2+y2 dz dy dxTo convert it into polar coordinateswe know thatx=rcosθ,y=rsinθ…

Q: Use Stokes' theorem to evaluate line integral| (z dx + x dy + y dz), where C is a triangle with…

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Q: Use Green's Theorem to evaluate the line integral: f. In(1 + y) dr – #, dy where C is triangle with…

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Q: Calculate line integral F-dr where F(x, y) = (7x + y, 5x + 2y) and C is a rectangle with vertices…

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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 evaluate the line integral [F•dš where F = 2xyi +(x– y²)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. yex dx…

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Q: Calculate the scalar line Integral where the function is f(x,y)= 1 / x²+y²+1 and the curve is the…

A: We have given function fx,y=1x2+y2+1 and the curve joining the point 0,0 1,0 1,1 0,1. Let A0,0,…

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

A: Formulae used, d(ex)dx=ex d(x)dx=1and         ∫abexdx=exab

Q: (०हागो 10,3,0)and (0,0,6). Tongular lamina with for of stokes deo theorem.

A: Given

Q: Verify the line integral and surface integral by relating them to the Stokes' Theorem where C is the…

A: Stokes theorem    ∫CF→.dr→=∫∫ScurlF→.dS→ Where S  be a smooth surface  bounded by a closed, smooth…

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

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Q: Use double integral polar coordinates to find the area of the portion of the surface 3z = xy that…

A: Area of the surface given by the equation z=fx,y is given by S=∫∫A 1+zx2+zy2 dA where A is the…

Q: Evaluate the line integral Fdr where F = 4.xyi – 8yj+ 3k and C is a curve given by y = 2x, z = 3…

A: Answer

Q: . Find the centroid of the solid generated by the area bounded by y = sin x and the lines x = 0; x =…

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Q: compute the line integral fc f (x, y) ds for th,e given function and path or curve. (a) f (x, y) =…

A: To compute the line integral  ∫Cfx,y ds where, fx,y=xy and the path of curve is rt= t,  2t-1…

Q: Using Stokes's theorem, calculate the line integral is the triangle with vertices (0,0,0), (1,0,0),…

A: To use Stokes's theorem to calculate the line integral of the below function. F=2y2, 3x2, z−x The C…

Q: Verify Stokes's Theorem by evaluating F. dr as a line integral and as a double integral. F(x, y, 2)…

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

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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: Evaluate the line integral Jxy + z)ds where c the arc of circle x + y = 4, z= 0 from (2, 0, 0) to…

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Q: Use Green's theorem to evaluate the line integral F•ds where F = 2xyi +(x-y')j and C is the %3D path…

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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: Calculate line integral F-dr where F(x, y) = (7x + y, 5x + 2y) and C is a rectangle with vertices 0,…

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Q: Use Stokes' theorem to calculate , F.ds, where F = (z, x, y) and C is the boundary %3D of a triangle…

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Q: Evaluate the integral ∫(1,2,3)(5,9,−4)y dx+x dy+2 dz by finding parametric equations for the line…

A: To evaluate the integral

Q: Use Stokes' Theorem to find the circulation of F = 4yi + 2zj + 4xk around the triangle obtained by…

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Q: Use Stokes' Theorem to choose the correct integral to evaluate the line integral…

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Q: Let F = 4(x + y) i + 8 sin(y) j. Find the line integral of F around the perimeter of the rectangle…

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Q: Find the line integral of z2 dx + y dy + 4y dz, where C consists of two parts, C, and C,. C, is the…

A: Given line integral ∫Cz2dx+ydy+4ydz, where C consists of two parts C1 and C2. C1 is the intersection…

Q: Evaluate the contour integrals cosh z dz 4z2 + 72 z +1 dz 223 – 322 – 2z and around the unit circle…

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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: 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,…