6. Evaluate the surface integral where o is the portion of the cone z = Vr? + y? between the planes z = 2 and z = 3.

Q: Evaluate the triple integral R. where R is the region enclosed by the sphere r2 + y² + 2? = 9.

A: If y=f(x), then the independent variable x is called the input of the function, and the dependent…

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

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: What is the volume of the solid enclosed by the planes z = 3 and x + y − z = −13, and the curves y…

A: Given,  The solid enclosed by the planes z = 3 and x + y − z = −13, and the curves y = x2 and x = y2

Q: Find the area of the portion of the cylindrical surface Y = 4 – x² in the first octant that is…

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Q: - Find the volume of the region cut from cylindrical (x² + y² = 16) by the plane z 0 and the plane…

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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: (b) Calculate the volume of the tetrahedron in the first octant bounded by the plane x + 2y + 3z = Q…

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Q: Find the area of the part of the plane  z = ax + by + c  that projects onto a region in the…

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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: Compute the area of the portion of the cone x2 +y = z2 with z z 0 that is inside the sphere x y z…

A: Given the area of the cone is x2+y2 = z2 and the sphere is x2+y2+z2 = 2Rz.

Q: Let S be the part of the hyperbolic paraboloid z = x2- y2 located between the cylinders x2 + y? = 1…

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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: Compute the triple integral f(x,v.z)dxdydz where D is the sphere with center O and radius R and…

A: Given that ∭Df(x,y,z)dxdydz where f(x,y,z)=R2-(x2+y2+z2). By the spherical coordinates,…

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: Reduce the surface integral ( S A.ds) of a cube of sides parallel to the three perpendicular axes,…

A: Here we can use divergence theorem to reduce the given surface integral. Divergence theorem states…

Q: Use the Theorem of Pappus and the fact that the volume ofa sphere of radius r  is 4/3πr3  to find…

A: We have, The volume of a sphere is V=43πr3                               ⋯⋯1. The semi-circular…

Q: Use the Divergence Theorem to evaluate the surface integral (2x^2 + 3yz + 4xz) dS where S is the…

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Q: (9) Evaluate the surface integral / S, czdS, where o is the part of the plane r+2y+3z = 6 that lies…

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Q: Compute the surface area of the domed structure D:= {(x, y, 2) ; x² + y² + (z – 1)² = 2 ; z > 0}.

A: x2 + y2 + (z-1)2 = 2  ,  x2 + y2 + (z-1)2 = 2  ,  z ≥ 0 This equation is for sphere of radius  = 2…

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: Calculate the area of the surface S. x2 that lies between z = 2 and z 6. S is the portion of the…

A: A coordinate system is a convention that is used to represent a point uniquely using a set of…

Q: 2. Fnd the area of the sur face in the first octant cut from the cone z2 = x2 y2 by the plane x +y =…

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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 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: 2. Find the volume of the region enclosed by the paraboloid z = x2 + y? and the plane z 2x.

A: Given paraboloid, z=x2+y2and the planez=2x To find the volume of region enclosed by the paraboloid…

Q: 5. Calculate the value of 7.îî dA over the whole surface of the cylinder bounded by x? + y? = 4, z =…

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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: 10. Determine the surface area of the part of z = xy that lies in the cylinder given by x² + y² = 1.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Use geometry to evaluate ∫∫∫R 1 dV where R is the region inside the sphere x2+y2+z2=4.

A: Given R as the region inside the sphere

Q: Find the surface area of the planez= x +y?from z=4 to z=9?

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Q: Find the volume of the solid inside the sphere p = 4 that is bounded above by the cone = T/3 and…

A: According to question, ρ = 4,ϕ = π3

Q: Show that the volume of the region bonded by the cone z = Vx² +y2 and the paraboloid z =x² +y is…

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Q: Find the area of the part of the plane 3x + 3y + z = 9 that lies inside the cylinder x2 + y2 = 25.

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Q: 10. Find the area of the paraboloid x² + y + z² = 2 by the plane y = 0. (Hint: Implicit Surface)

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Q: Find the volume of the solid bounded by the paraboloid z = 16 – x2 – y?, the cylinder x2 + y? = 8…

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

A: Answer

Q: (b) Find the volume under the paraboloid z=x+y² above the triangle enclosed by the lines y=x, x=0…

A: To find the volume of the given solid.

Q: Find the surface area of the plane 3x + 2 y + z = 6 that lies in the first octant.

A: The surface area of the plane z=f(x,y) is given by the formula                          S=∬D…

Q: Calculate the area of the surface S. x2 y² _ z2 that lies between z = 2 and z = 6. S is the portion…

A: Explained below

Q: Let S be the hemisphere x2+y2+z2=4, with z≥0. Evaluate the surface integral   ∬S z2 dS

A: we have the hemisphere x2+y2+z2=4with z≥0    we have to evaluate the surface integral ∫∫sz2ds so, we…

Q: 8. Show that the volume of the region bonded by the cone z = Vx² + y² and the paraboloid z = x? + y²…

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Q: 1. Find the surface area of the cone z = √x² + y² that lies between the plane y = x and the cylinder…

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Q: The volume of the solid enclosed by the surface z = 1/y and the rectangle 2 <r<4, 1<y<e in the…

A: We use double integral to find the volume of the solid.

Q: Evaluate the surface integral (4x² + 3y)dS where S is the part of the plane 2.x + 5y + z = 48 inside…

A: We need to calculate:∬S4x2+3ydS over the surface S,which is the part of plane 2x+5y+z=48, inside the…

Q: Let Ss be the portion of the cone z = Vr2 + y? – 4 (i.e. z = -4 + Vr² + y?) that lies below the…

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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: Find the surface area of z =1-(x^2)-(y^2) that is above the xy plane

A: Given equation of plane is  z=f(x,y)=1-x2-y2 we have to find the surface area above xy plane.

Q: 6. Compute the volume of the solid that lies above the paraboloid z = r² + y? and below the…

A: Given: z=x2+y2z=x2+y2