Let E be the solid region in the first octant bounded by the coordinate planes, the cylinder x2+y2=5y and the sphere x2+y2+z2=25. Write an interated intergral used to solve ∫∫∫Ey dV using:  A. Cartesian coordinates B. Cylindrical coordinates without evaluating.

Q: Evaluate the surface integral F. dS where F = (4x, -5z, 5y) and S is the part of the sphere x² + y +…

A: The solution is given below:

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

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Q: Use a change to spherical coordinates to evaluate L Vx² + y² + z² dV , where E is E the region…

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Q: Evaluate f, A.n ds, where A = zi +j- 3y²zk and S is the surface of cylinder x? + y? = 16 included in…

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Q: Evaluate fff 1- x2 - y2-z2 dx dy dz where V is the volume of the sphere x? + y? + z2 = a? by…

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Q: Use the cylindrical coordinate to evaluate ſSS, x² + y?dV where G is the solid bounded by xy-plane…

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Q: Evaluate [f[(x² +y² +=?)2 dV, where 2 is the solid hemispi sphere) enclosed by x +y +z =1 and above…

A: We have to choose the correct answer from the given options

Q: Evaluate the triple integral. SII ydV where G is the solid enclosed by the plane z = y, the…

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Q: Compute the volume of the solid bounded by the hemisphere z = the horizontal plane z = c by using…

A: To compute the volume of the spherical cap, use the following formulae and convert the Cartesian…

Q: Find the volume of the solid generated by revolving the curve y - 1* – 1 = 36 between z =0 and z=1…

A: Given that  Curve y^2-x^8-x^2=36 From x=0 to x=1  Find the volume of the solid

Q: Use cylindrical coordinates to evaluate the triple integral E Va2 + y? dV, where E is the solic 16…

A: use cylindrical coordinates of find the volume

Q: b) Using Spherical Coordinates, find the volume of the solid G bounded above by the sphere x2 + y? +…

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Q: 1. Compute the volume of the solid bounded by the hemisphere z = √√4c²-x² - y² and the horizontal…

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Q: Use polar co ordinates to find the volume of the given solid  above the cone z=sqrt{x^2+y^2} and…

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Q: Use polar coordinates to find the volume of the given solid. Bounded by the paraboloid z = 5 + 2x2 +…

A: We have to find volume of paraboloid in the first octant-

Q: Given F = xi - yj, find the value of ∬F • n dS over the closed surface bounded by the planes z = 0,…

A: According to the given information,

Q: Evaluate , x*+2y* D 2x++8y++2z+ dV, where D is the region enclosed by the spherical surface x2 + y?…

A: Given: To evaluate ∫∫∫D x4 + 2y42x4  + 8y4 + 2z4 dV  Where D is the region enclosed by the spherical…

Q: Evaluate the triple integral. [l ydV where G is the solid enclosed by the plane z = y, the xy-plane,…

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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: e of the solid E whose boundaries are given in rectangular located inside the circular cone x? + y?…

A: In this question we will use basic of calculus i.e volume of cone. We will simply draw the given…

Q: Use cylindrical coordinates to evaluate SI vz dv where E is the solid E bounded by the cylinder,…

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Q: Use polar coordinates to find the volume of the solid under the paraboloid z = 4 – x2 y' and above…

A: a)  Given that z=4-x2-y2and the disk(x-1)2+y2=1 To find the volume under z over the given disk by…

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

A: We need to find the integral , ∭D y2 dV   where D is the tetrahedron in the first octant bounded by…

Q: nd the volume of the solid bounded by the paraboloid z = 32 – x² – y², the cylinder r² + y? = 16 and…

A: The solution are next step

Q: Consider the paraboloid z = 1- ² – y?. Find the volume of the region between this surface and the ry…

A: According to the problem,. we have

Q: Find the surface area of the part of the circular paraboloid z = x + y that lies inside the cylinder…

A: Solve the given

Q: Convert into cylindrical coordinates. Tis in the First Octant bounded by Z = 3√x²+4/² Z SS S dy √x²…

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Q: Let G be the solid in the first octant bounded by the sphere 2x? + 2y? + 2z? = 32 and the coordinate…

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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: Let E be the solid ellipsoid bounded by the surface y? = 1, a2 62 c2

A: Given that, the solid ellipsoid bounded by the surface x2a2+y2b2+z2c2=1 The volume of the unit…

Q: Evaluate dV, where E lies between the spheres x + y² + z? = 16 and E x2 + y2 + z2 r + y + z 64 in…

A: Follow 2nd ,3rd step .

Q: Evaluate dV, where E lies between the spheres x2 + y? + z2 = 4 and x? + y? + z² E x² + y? + z? = 36…

A: x​=ρcosθsinϕ y=ρsinθsinϕ z=ρcosϕ ρ2 = x2+y2+z2 ​

Q: Use cylindrical coordinates. JSS x² + y2 dv, where E is the region that lies inside the cylinder x²…

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Q: b) Using Spherical Coordinates, find the volume of the solid G bounded above b x² + y? + z? = 25 and…

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Q: Use polar coordinates to find the volume of the solid under the paraboloid z=x2+y2 and above the…

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Q: Let G be the solid which lies above the plane z = V3 and within the sphere x² + y? + z2 = 4. Suppose…

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Q: Find the surface area of the part of the hyperbolic paraboloid z = y? –x² that lies between the…

A: Given The hyperboloid z=y2-x2 that lies between the cylinders x2+y2=1 and x2+y2=4.

Q: Let G be the solid in the first octant bounded by the sphere 2x? + 2y? + 2z? and the coordinate…

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Q: Use polar coordinates to find the volume of the solid under the paraboloid z = x2 + y2 + 1 and above…

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Q: Calculate by changing to cylindrical coordinates the integral x² + y² dxdydz, where N is the domain…

A: The solution are next step is

Q: SSS, xz dV, where D is the solid region in the first octant bounded above by the sphere x + y2 + z?…

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Q: If E is the region inside the sphere x2 + y² + z² = 4, below the cone z = V3x2 + 32, above z = 0 and…

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Q: Use spherical coordinates to evaluate the triple integral [[[ 2² + 3² + 2²dV, where E is the ball:…

A: We will first change it into spherical coordinate and then solve it.

Q: Find the volume of the solid that lies under the elliptic paraboloid z = 3y? – a? + 4and above the…

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Q: Use polar coordinates to determine the volume of the given solid Under the paraboloid: z = 18 – 2x?…

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Q: Find the surface area of a) The part of the plane 3x + 2y +z = 6 that lies in the first octant b)…

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: Let S be the solid obtained by rotating the region shown in the figure below about the y-axis. y…

A: The function of the curve is y = 6x(x-1)2.

Q: 17. Let T be the solid bounded below by the half-cone z = Vr2 + y? and above by the spherical…

A: Consider T be the solid bounded below by the half cone z=x2+y2 and above by the sphere x2+y2+z2=1.…

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: Use spherical coordinates to evaluate the triple integral e-(x² + y² +2²) J dV, x √2² + y² + 2² E…

A: