Compute the surface integral over the given oriented surface: F = y°i+3j – xk, portion of the plane x + y + z = 1 in the octant æ, y, z > 0, downward-pointing normal l, F· dS =

Q: Use Stokes' theorem to evaluate the surface integral I of the two-form w = dŋ, with n = (xz+ yz²) dæ…

A: η=(xz+yz2)dx+(sin(y)+z+5x)dy+xyz dzz=13-x2-y2,   z≥9 F→=xz+yz2i+(sin(y)+z+5x)j+xyzk z=9⇒9=13-x2-y2…

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: Evaluate the surface integral. xz ds S is the boundary of the region enclosed by the cylinder y? +…

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Q: Evaluate the surface integral (x - z) dS where S is the portion of the cylinder r +z? = 1 above the…

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Q: Let S be the part of the cone z = Vx2 + y? under the plane z = 4, outside the cylinder +y 1, and in…

A: The given cone is where  The widest section of the surface is obtained at z=4, whereas the thinnest…

Q: Find the surface area generated by rotating y=sin x. 0 ≤ x≤ π about the x-aixs.

A: Area of surface problem....

Q: Evaluate the surface integral. xyz ds, S is the cone with parametric equations x = u cos(v), y = u…

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

Q: Consider the surface S which is the part of the cylinder x^2 + z^2 = 9 , whit   0 ≤ y ≤ 2; x ≥ 0; z…

A: a  x2+y2=9    0≤y≤2,  x⩾0, z⩾0   S is parametrised by     rθ,y=3 cos ϖ, y, 3 sin θ    θ∈0 π2,   y∈0…

Q: Compute the surface integral over the given oriented surface: F=y³i+7j − xk, portion of the plane x…

A: We need to find surface integral.

Q: Find the area of the surface generated by revolving the curve a. y = V1+ e* between x = 0 and x = 1…

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Q: Evaluate the surface integral. dS S is the part of the sphere x2 + y² + z? = 16 that lies inside the…

A: The objective is to find the surface integral  ∫∫Sy2dS  where S is the part of the sphere…

Q: Evaluate the surface integral. The double integral over S (xz) dS, S is the part of the plane…

A: Evaluate  the surface integral for the function2x+2y+z=4

Q: Compute the surface integral over the given oriented surface: F= y'i + 6j – zk, portion of the plane…

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Q: Compute the surface integral over the given oriented surface: F = y²i + 6j − xk, normal F. ds =…

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Q: Evaluate the surface integral. xz dS S is the boundary of the region enclosed by the cylinder y? +…

A: The region of integration is bounded by three surfaces S1: y2+z2=64, S2: x=0 and S3: x+y=9. From the…

Q: Compute the surface integral over the given oriented surface: F = y²i+6jxk, portion of the plane x +…

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Q: (b) Use Stokes' Theorem to find the surface integral over the positively oriented upper hemisphere…

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Q: Find the surface integral ls yz dS, where S is the plane surface z = x + 3y lying above the…

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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: * Evaluate the surface integral SS F - d§, where F = z7 + y²7 + z² and S is the boundary of the…

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Q: Use a surface integral to calculate the area of the disk S given by z = 5 − y that lies inside the…

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Q: Evaluate the flux integral F.S where S is the surface given by 22 = a? + y?, 0 <z< 4, oriented…

A: The given problem is to evaluate the given flux integral of the given vector field over the given…

Q: The portion of the surface h x² + y? with h, a > 0, 2 = -. a between the ry-plane and the plane z =…

A: Given that:   The portion of the surface is given as: z=hax2+y2  with h,a&gt;0

Q: Use​ Pappus's theorem for surface area and the fact that the surface area of a sphere of radius a is…

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Q: Evaluate the surface integral || x2 z2 dS, where S is the part of the cone z2 = x² + y?, S that lies…

A: Here we solve the given problem of calculus.

Q: Evaluate the surface integral (image) whre S is the cone paramterized by x = ucos(v), y = usin(v),…

A: Here, x=ucosvy=usinvz=u0≤u≤10≤v≤π2

Q: The surface integral A. dS where Ā = xi+yj+zk closed surface S is defined by sphere

A: Introduction __:

Q: Evaluate the surface integral of G(x, y, z) = z - y over the surface S, where S is the portion of…

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Q: Choose the correct integral to evaluate the surface integral (x+y)zdS,where S is the portion of the…

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Q: Compute the surface integral over the given oriented surface: F = (0,0, e+z), boundary of the cube 0…

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Q: Evaluate the integral //, (x² + y²) dA where R is the quarter disk of radius 3 centered at the…

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Q: Find the volume of the solid that lies under the surface z = 4 +y and above the region D in the…

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Q: Compute the surface area of the cone with parametrization p(r, 0) = (r cos 0, r sin 0, r) where 0 <…

A: Formula Used:- Surface Area is given by For ϕ(u, v)=&lt;p, q, r&gt;Surface Area =∬ ||φu×φv|| dudv

Q: Evaluate the surface integral , F· dS where F = (4x, –4z, 4y) and Slis the part of the sphere x2 + y…

A: Answer

Q: Use Stoke's Theorem to evaluate the line integral / 7ydx + 3zdy + dz where C is the intersection of…

A: Use Stoke's Theorem to evaluate the line integral ∫C7y dx+3z dy+ dz, where C is the intersection of…

Q: Find the surface area of the cone z = ' + y² that lies between the plane y = x and the cylinder y =…

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Q: Find the polar moment of inertia of the region in the xy plane bounded by x2 - y2 = 1,x? y²=9,xy =…

A: Given: To explain the given statement as follows, To find : the polar moment of inertia of the…

Q: 6. Evaluate the surface integral where o is the portion of the cone z = Vr? + y? between the planes…

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Q: Compute the surface integral over the given oriented surface: F = (0,6, x²), hemisphere ? + y² + z²…

A: Given function is F=0,6,x2 To find the surface integral of the above function over the below…

Q: Find the exact area of the surface obtained by rotating the given curve about the x-axis. x = acos'…

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Q: Evaluate the surface integral //, 2zdS where S is the portion of the paraboloid 2z = 1+ x2 + y² in…

A: Given paraboloid is 2z=1+x2+y2 in the first octant bounded by x=0,y=3x,z=1 The surface of the…

Q: Evaluate the line integral S.F · dr where F(x,y, z) = x³i – y²j+ zk and C is the poundary of the…

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Q: use the Causs theorem to reduce the surface integral (JA.ds) on all six faces of a cube whose volume…

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Q: Evaluate [F d$ for F = yi+=j+2xk and S is a surface of the region bounded by the cylinder x+ y = 4…

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Q: Evaluate the surface integral [(xz + y* ) ds where s is the surface of the XZ- cylinder y + z? =…

A: Consider the provided question,

Q: Consider the integral 2zx? dx dy dz, where N is the domain bounded from below by the cone z = by the…

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Q: Evaluate the flux integral , curl (z cos x î + y j+ x sin y k) dS where S is the part of the outward…

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Q: Evaluate the surface integral. SS, xz ds, S is the part of the plane 2x + 2y + z = 4 which is in the…

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Q: Determine the volume enclosed between the hemispherical surface z=f(x,y)=9−x2−y2−−−−−−−−−−√ and the…

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Q: Evaluate the surface integral. (x²z. y?z) as x2z + S is the hemisphere x2 + y2 + z² = 4, z 2 0

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