Evaluate the surface integral + y² + 6z² ) d$ where S is the part of the cone z = 6 - Vx? + y above the z = 0 plane. The surface integral equals|

Q: Use spherical coordinates to find the volume of the solid bounded above by the sphere p = 4 and…

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Q: Evaluate the surface integral LL 6xzdS where S is the part of the plane 2x + 2y + z = 4 that lies in…

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

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Q: Find the area of the surface of revolution r(u, v)= 6sin(u)cos(v)i+ 6uj+6sin(u)sin(v)k, where 0SusT…

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

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Q: Evaluate the surface integral f F. dS where F = (-2x, –5z, 5y) and S is the part of the sphere x2 +…

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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: Evaluate the double integral V1 + 4x² + 4y²dA, where D is the region inside the circle x + y? = 25…

A: We have to find area of the region bounded by the circle given in the first quadrant of the plane.

Q: What is the center of gravity of the solid formed when the plane region bounded by y = x^2 and y=x+2…

A: We sketch the given region using a graphing calculator as shown below:   The shaded region is…

Q: Set up, but do not evaluate, an iterated integral that equals the surface integral |/ (2² – y²) dS,…

A: Given data:   The given surface integral is I=∫∫S(z2-y2)dS. The given part of the cone is…

Q: Evaluate the surface integral. (x²z + y²z) dS Is S is the hemisphere x2 + y2 + z2 = 9, z 2 0

A: Given:      ∫∫Sx2z+y2zdS    where S is the hemisphere x2+y2+z2=9 , z≥0   Parameterize the hemisphere…

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

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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: Find the surface area of the part of the plane z = 5 + 7x + 2y that lies inside the cylinder a2 + y?…

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Q: 2. Use a parametrization to express the area of the given surface as a double integral and then…

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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: 2. Let S be the surface of the hemisphere, x2 + y² + z? = 4; z > 0. Evaluate the following surface…

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Q: Find the surface area of that part of the plane 9x + 6y + z = 4 that lies inside the elliptic…

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Q: Evaluate the surface integral. 2,2 ds S is the part of the cone + y that lies between the planes z =…

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Q: Use spherical coordinates to find the volume of the solid G bounded above by the sphere x² + y² + z²…

A: Given that the solid inside the sphere is x2+y2+z2=16 and  the cone is z=∠x2+y2we need to find the…

Q: Evaluate the surface integral fs F. dS where F = (-2x, –5z, 5y) and S is the part of the sphere x? +…

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Q: Evaluate the surface integral. y² ds, S is the part of the sphere x² + y² + z² = 1 that lies above…

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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>0

Q: (b) Verify Stokes' theorem on a region which is a portion of the sphere x? +y? +z² = 16 which lies…

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Q: Write the integral fS Sw ela+y²+z*)8/² dV_where W is the portion of the solid sphere a? + y? + z? <…

A: ANSWER :

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: (a) Evaluate the following surface integral yex²+z² dS, where o is the portion of the surface of the…

A: Given the integral ∬σyex2+z2dS we have evaluate the given surface integral where σ is the portion of…

Q: Find the volume of the solid bounded by the paraboloid z = 2 – 4x? – 4y? and the plane z =

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Q: nd the surface area of the part of the plane z + 4y + z = 2 that lies inside the cylinder r +y° = 9…

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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: Find the surface area of the cone z = x² + y2 that lies between the plane y = x and the cylinder y =…

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Q: Evaluate the surface integral. I. (2z + v²z) ds S is the hemisphere x2 + y2 + z2 = 4, z 2 0 %3D

A: The objective is to evaluate the surface integral,  ∫∫Sx2z+y2zdS where S is the hemisphere…

Q: set up, do not evaluate, the double integral for the surface area of the portion of the paraboloid…

A: The solution are next step

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

A: Evaluate the surface integral.

Q: 2. Use a parametrization to express the area of the given surface as a double integral and then…

A: Given ,x2+y2+z2 = 22       _________(I)and z = x2+y2     __________(II)Putting the value of z from…

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

A: Answer

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: Q4. Evaluate the surface integral ,(x² + y²)z dS, where o is the portion of the sphere x² + y? + z?…

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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: What is the center of gravity of the solid formed when the plane region bounded by y = x, y = 2x,…

A: Let us start solving the problem step by step

Q: Use spherical coordinates to find the volume of the solid bounded above by the sphere p = 4 and…

A: Solution is in step 2

Q: Jevaluate the surface integral ff, (y²z2 i+ z?x² j+ z²y²k).n ds, where S is the part of the sphere…

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Q: Evaluate the surface integral a dS where S is the entire surface of the solid bounded by the…

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Q: Find the area of the surface obtained by rotating thecircle x2 + y2 = r about the line y =r.

A: We have to find the area of the surface obtained by rotating the circle x2 + y2 = r about the line y…

Q: need ASAP B. Find the area of the portion of the cylindrical surface y = 4 − x2 in the first…

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Q: Evaluate the surface integral s F. dS where F (-x, -4z, 4y) and S is the part of the sphere x? + y?…

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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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Q: Let S denote the part of the cone x? + y = z² that lies between the planes z = 2 and z = 3+ x,…

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