Please show all the necessery steps. Thanks. Let D be the unit disk D= { (x, y) : 0 < x² + y² < 1}. Evaluate e²+y´ dA.

Q: Use spherical coordinates to evaluate // | eva*+*** dV, where E is enclosed for E by the sphere x² +…

A: Please see the below picture for detailed solution.

Q: Use spherical coordinates. Evaluate ∭e ^ (x ^ 2 + y ^ 2 + z ^ 2) dV, where E is inside the sphere x…

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Q: 1 in 1in y 1 in 3 in 1 in X

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

Q: Use spherical coordinates to evaluate f[[, 3e(a+y´+z²)°/² dV, where E is the region inside the…

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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: Use spherical coordinates. Evaluate ∭z dV, where E is between the spheres x ^ 2 + y ^ 2 + z ^ 2 = 16…

A: Triple integral is used to integrate function of three variable in three dimensional region.

Q: Evaluate || zdS, where S is the surface whose: S Sides S1 are given by the cylinder x? + y? = 1,…

A: It is given that: Side S1 are given by the cylinder x2+y2=1 Bottom S2 is the disk x2+y2≤1 in the…

Q: S* ds. x* + y+z*= x+y - Evaluate where S is the part of the sphere that lies above the cone

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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 ze*²+y²+z? dV, where E is the portion of the ball centered at the origin of radius 5, x2 +…

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Q: Evaluate [[[(x2 + y² +z?)2 dV, where 2 is the solid hemisphere (half of the sphere) enclosed by x +…

A: Apply the spherical coordinate to find the volume integral, x=ρsinφcosθ ; y=ρsinφsinθ ; z=ρcosφ And,…

Q: Find the area of the surface given by  r(u,v) = (u+v,u,v) 0 ≤ u ≤ 1, 0 ≤ v ≤ 1

A: Given ru,v=u+v, u, v0≤u≤1 , 0≤v≤1

Q: Find the area of the plane xtay-zt 10=0 that lies above the disk xy-plare

A: Given that, Area of plane is x+2y-z+10=0 It lies above the disk {(x,y)/x2+y2≤4} in x,y plane. The…

Q: Use spherical coordinates. Evaluate (x2 + y2) dv, where E lies between the spheres x² + y2 + z² = 9…

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Q: Let NR be a disc with centrum in origo and radius, R. 1 Assume that, J(x, y) x² + y? < R². 1+x2 + y²…

A: ΩR be a disk with centrum in origo and with radius, R. Assume that, Jx,y=11+x2+y2,x2+y2≤R2. Then we…

Q: | a2 dA, where D is the part of the unit disk where r+y 2 0.

A: To find :         ∬Dx2 dA where D is the part of the unit disk where x+y≥0

Q: Use spherical coordinates. Evaluate |/| (x2 + y²) dv, where E lies between the spheres x2 + y2 + z2…

A: For spherical coordinates: x = ρ sinφ cosθ, y = ρ sinφ sinθ z = ρ cosφ. So,       x2+y2=ρ sinφ…

Q: Find the area of the surface. The part of the sphere x² + y² + z² = 36 that lies above the plane z =…

A: Consider the sphere x2+y2+z2=36 For z=3, the projection of the part of the sphere in the xy-plane…

Q: The area of the surface p = 2, 0sz<5,0<¢< T is 201 Select one: O True O False

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Q: Verify Stoke's for F = (2x – y)i – yz²j – y²zk where S is the upper half of the sphere x? + y? +z² =…

A: Solution is given below

Q: AP where R is the portion of the ball of radius 1 in 4-dimensions with all coordinates r, y, z, w 2…

A: I = ∫∫∫R∫ dvwhere R = portion of unit ball with x, y,z,w≥0I = ∫01∫01∫01∫01 dx dy dz dw= ∫01∫01yo1 dz…

Q: dx dy, where D is the disk x2 + y² < 9. (x² + y?)3/2 Evaluate

A: The given integral is,

Q: Use spherical coordinates. SI. Evaluate Vx2 + y2 + z2 dV, where E lies above the cone z = Vx2 + y2…

A: The spherical coordinate system is a polar coordinate system used to translate cartesian plane to…

Q: Use spherical coordinates. Evaluate z dv, where E lies between the spheres x2 + y2 + z² = 1 and x2 +…

A: Using spherical  coordinate we can solve it very easily.

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: Evaluate z* + x dS where S is the cylinder x2 + y? = 36 between the planes z = -3 and z = 1,…

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Q: Verify Stoke's for F = (2x – y)i – yZ“]-y-zk where S is the upper half of the sphere x2 + y² + z² =…

A: Here verify Stoke’s theorem in the vector F = (2x –y) i – yz2 j – y2z k Where S is the upper half of…

Q: Use cylindrical coordinates. Evaluate z dV, where E is enclosed by the paraboloid z = x2 + y2 and…

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Q: Let B be the ball with center at the origin and radius 1 I//3(x² + y + z?)dV =

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Q: Evaluate I ( V9 - x2 - y2 dA, where D is the disk x? + y < 9, by interpreting it as a known volume.…

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Q: y 2 2 2 4

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Q: EX. Find the volune of the solid region lymg mside both the sphere Xtuf+2?= 402 and the cylmeder…

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

Q: Use spherical coordinates. Evaluate z dv, where E lies between the spheres x2 + y2 + z2 = 9 and x2 +…

A: Given equations of spheres: x2+y2+z2=9 x2+y2+z2=36 For spherical coordinates: x=ρ cosθ sinϕy=p sinθ…

Q: When the shaded region is rotated around the y-axis, a horizontal strip of vertical span Ay creates…

A: We have to find the volume V of the solid obtained by rotating the region bounded by the given…

Q: Use spheri\cal coordinatcs Evaluate y'zdV, where E lies above the cone 4 = /3 and below the Sphere…

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Q: O 9/ Compute I - [.lryz) , uhere s is the part g the plane y +x that lies inside the half-cylinder…

A: We know that, dS=1+∂z∂x2+∂z∂y2dydx where S is the part of plane z=y+x. ∂z∂x=1∂z∂y=1 dS=1+(1)2+(1)2…

Q: (a) Evaluate (x? + y?)" dA where R is the unit disk r2+ y? < 1.

A: The solution is given as

Q: Use spherical coordinates. SIL Evaluate xyz dV, where E lies between the spheres p = 2 and p = 6 and…

A: Consider the given statement. Let  x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ Then dV=ρ2sinϕdρdθdϕ The limits…

Q: Evaluate [[[ =*dxcydz over the sphere x +y² +=² =1.

A: to find:- to evaluate the given integral.

Q: Using the spherical coordinate evaluate a) ,x² dv, where G is a solid region between the sphere x² +…

A: The given integral is ∭Gx2 dV where G is a solid between the sphere x2+y2+z2=4  and x2+y2+z2=9.…

Q: Use cylindrical coordinates. Evaluate z dv, where E is enclosed by the paraboloid z = x2 + y² and…

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Q: SSx x dA; R is the portion of the disk x + ys 16 in the second quadrart

A: I use polar conversion method

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

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Q: Use spherical coordinates. SIL Evaluate (x2 + y2) dv, where E lies between the spheres x² + y2 + z²…

A: Consider the given integral ∫∫∫Ex2+y2dV, where E lies between the spheres x2+y2+z2=4  and…

Q: For numbers 45 and 46: Let D be the disk with center the origin and radius 3. Consider the double…

A: In polar co-ordinate system, x=rcosθ and y=rsinθ also dA=rdrdθ . The limit for r is 0≤r≤3 and for θ…

Q: Find the average distance from a point P(x, y) in the disk x2 + y2&lt;=a2 to the origin.

A: Average distance is given as

Q: Use cylindrical coordinates. Evaluate z dV, where E is enclosed by the paraboloid z = > =x² + y2 and…

A: Consider the triple integral,∭ e zdvHere E is the region enclosed by the plane z=4 and the…

Q: Let S be the sphere x + y² + z? = 9 oriented outwards, and F = (5x, 7z, –3y). Evaluate: F. dS. The…

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Q: Use spherical coordinates. y2 + z2 where E is enclosed by the sphere x2 + y? + z = 49 in the first…

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Q: The spheres x² + y² + z² = a² and (x − b)² + y² + z² = (b − a)² are tangent at the point ○ (−6, 0,…

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