Evaluate z* + x dS where S is the cylinder x2 + y? = 36 between the planes z = -3 and z = 1, including the top and bottom sides of the cylinder.

Q: 7) z dV, E is the solid enclosed by the cylinder r2 +y = 1, and the E planes z = 0 and z 3.

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Q: Use Cartesian coordinates to evaluate JIJ y² dv 2 D where D is the tetrahedron in the first octant…

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A: Consider the diagram and divide into four regions as shown below, Now, make a chart and evaluate…

Q: Use cylindrical coordinates. Evaluate II Vx2 + y2 dv, where E is the region that lies inside the…

A: Volume using triple integral

Q: Find the surface area of the part of the plane z = 5 + 7x + 2y that lies inside the cylinder x² + y?…

A: Part of the plane is z = 5 + 7x + 2y, so this is given in terms of f(x,y). If part of the plane is…

Q: The axis of symmetry of the cylinder is parallel to the z-axis. х-ахis. O y-axis.

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Q: Find the area of the part of the hyperbolic araboloid z = y² – x² nat lies between the cylinders x²…

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Q: Evaluate fS f3zdV E where E is the solid enclosed by z= 1 a2 + y? and z =

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Q: Evaluate fR z = Jx2 + y2 x2 + y2 + z2dxdydz, where r is the region bounded by the plane z = 3 and…

A: We will convert integral into spherical co ordinate system . 1st relation between cartesian and…

Q: Find the angle between the planes 3x – 2y + z + 4 = 0 and x + 4y – 3z – 3 = 0. Express your answers…

A: The angle between two planes is equal to the angle between their normals.

Q: Use cylindrical coordinates. Evaluate III Vx2 + v² dV, where E is the region that lies inside the…

A: We have to evaluate ∭Ex2+y2dV, where E is the region that lies inside the cylinder x2+y2=9 and…

Q: Use cylindrical coordinates. Evaluate IIL Vx²+ y2 dv, where E is the region that lies inside the…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Find the surface area of the part of the plane 2x+2y +z=4 that lies inside the cylinder x²+y² = 2.…

A: Given that, the equation of the plane is 2x+2y+z=4 and the equation of the cylinder x2+y2=2. Note…

Q: The solid bounded by x = y? – 1, z = 1 – y², z = 4 – x, and z = 0.

A: Given that,

Q: Considering f(x, y, z) = z + x²y and S as part of the cylinder y? + z² = 25 that is between the…

A: Given that, fx,y,z=z+x2y and S is the part of the cylinder y2+z2=25 that is between the planes x=0…

Q: Evaluate I/| V x2 + y² dV, where E is the region that lies inside the cylinder x2 + y? = 16 and…

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Q: Use cylindrical coordinates. Evaluate II V² + y2 dV, where E is the region that lies inside the…

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Q: Evaluate II Væ² + y? dV, where E is the region that lies inside the cylinder æ2 + y² = 16 and…

A: E is the region that lies inside the cylinder x2+y2=16 and between the planes z=-5 and z=4 Change…

Q: Evaluate z² dv. where E is the region above the zy-plane below the cone z = 2+2 and inside the…

A: The given problem is to evaluate the given triple integral over the given region E bounded above by…

Q: Evaluate y-dV, where E is the solid that lies within the cylinder x+y = 49, %3D above the plane z =…

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Q: Use cylindrical coordinates. Evaluate x2 + y2 dV, where E is the region that lies inside the…

A: The integral given is ∫∫∫E x2+y2 dV For the cylindrical coordinates x=r cos(θ)y=r sin(θ)z=zdV=r dz…

Q: Evaluate TI Vx + y2 dv, where E is the region that lies inside the cylinder x2 + y? = 1 and between…

A: In this question, we have to evaluate the triple integral by using cylindrical coordinates.

Q: Evaluate JJJ, (x² + y²)dV where D is the region that lies above the cone z = c/x² + y2 and inside…

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Q: Use cylindrical coordinates. Evaluate Vx2 + y2 dv, where E is the region that lies inside the…

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Q: Evaluate ||| Vx2 + y2 dV, where E is the region that lies inside the cylinder x2 + y? = 25 and…

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Q: Use cylindrical coordinates. Evaluate V x2 + y2 dV, where E is the region that lies inside the…

A: ∫∫∫E x2+y2 dv= ∫∫∫ x2+y2 dx dy dzPut                   | Thenx = r cos θ     | dx dy = r dr dθy = r…

Q: The base of a solid is bounded by y= x² and y= 4. All parallel cross – sections are squares…

A: Please rate

Q: Use cylindrical coordinates. Evaluate | Vx²+ y2 dV, where E is the region that lies inside the…

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Q: Use Cartesian coordinates to evaluate JIJ y² dv D where D is the tetrahedron in the first octant…

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Q: JJ F- ndS if F= xi + yj+(z² –1)k Evaluate and o is the curved surface of the cylinder y = V4-x? from…

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Q: Calculate xz dS, where S is the cylinder (including the top and bottom) x + y = 16, 0 < z < 5. %3D

A: answer is in next step

Q: H.W: Find volume of box (parallelepiped) determined by u = i+j- 2k, v = -i - k and w = 2i+ 4 j - 2k

A: Solution:-

Q: Evaluate I/ V x2 + y2 dv, where E is the region that lies inside the cylinder x? + y2 = 9 and…

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Q: The solid S above the surfaces 22 = + y? and below r +y +(2 - 5)2 = 25. 2 + y² + (2 - 5) = 25

A: Solution is below.

Q: Evaluate x2 + y? – z dS where S is the | S part of the cone z² = x² + y² that lies between the…

A: Given, f(x,y,z)=x2+y2-z Here, S is the part of the cone z2=x2+y2 that lies between the planes z=1…

Q: Integrate g(x, y, z) = x4y(y2 + z2 ) over the portion of the cylinder y2 + z2 = 25 that lies in the…

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 8x + 16y + 24z on the elipse…

A: To determine the maxima and minima of the function f(x, y, z) with respect to the function is…

Q: 5) 2z dV, E is the solid enclosed by the cone % = Vr2 + y? and the E plane z 5

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Q: The solid inside the cylinder x² + y? = 4 that is above by the planes z = 3 – x and below by z = x –…

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Q: Use cylindrical coordinates. Evaluate II| Vx² + y2 dv, where E is the region that lies inside the…

A: We have to evaluate  ∭Ex2+y2dV, where E is the region that lies inside the cylinder x2+y2=1 and…

Q: Let S denote the part of the cylinder x2 + y² = 9 that lies between the planes r + y = 1 and x – y =…

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Q: =+ x²y) ds part of the cylinder y² + z² = 9 that lies between the planes x = 0 and x = 3 in the…

A: See the details solution in below

Q: Find the area of the part of the plane 2x + 4y + z = 1 in the first octant. Select one: O a. V17 25…

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Q: 2y do over the surface S: z = ; 0<x< 2, 0<y<3 Evaluate

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Q: Find the area of the part of the paraboloid x = y2 + z2 that lies inside the cylinder y2 + z2 = 1

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Q: Use cylindrical coordinates. Evaluate x² + y2 dV, where E is the region that lies inside the…

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Q: Evaluate III Vx2 + y² dV E where E is the region that lies inside the cylinder x2 + y2 = 4 and…

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Q: Use Cartesian coordinates to evaluate Jff v² av D where D is the tetrahedron in the first octant…

A: Let us consider the integartion I=∫ab∫f(x)g(x)∫p(x,y)q(x,y)F(x,y,z)dzdydx To solve the integral…

Q: Find the area of the part of the cone S = {(x, y, 2); z = Vx² + y?, x²+y² < 1}.

A: Given surface is S=x,y,z:z=x2+y2,x2+y2≤1 We have to find the area of the surface. Here, z=x2+y2…

Q: Evaluate ||/ Væ² +y? dV, where E is the region that lies inside the cylinder æ² + y² = 16 and…

A: Given :  The integral ∫ ∫ ∫E x2+y2 dV , where E is the region that lies inside the cylinder  x2+y2 =…