1 Evaluate dV, where E lies between the spheres a? + y? + z? 25 and + y² + z? x² + y? + z? = 36 in the first octant.

Q: Evaluate ||E y²z² dV, where E lies above the cone o and below the sphere p = 1. = T/3

A: Given, ∫∫∫Ey2z2dV   ....(i)Let x=ρsinϕcosθ y=ρsinϕsinθ and z=ρcosϕAnd we know…

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: The value of the triple integral 22 zdV where E is the upper E half of the sphere of x² + y? + z? =…

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Q: Evaluate J₁ 1 E x² + y² + z² x² + y² +2²= 25 in the first octant. dV, where E lies between the…

A: Here we need to use spherical co ordinate system to find value of integral  Relation between…

Q: W hich of the following is not a cylinder? Justify your answer. y? +z?=2y

A: Given- y2+z2=2y To Find- Whether the above equation represet cylinder or not. Concept Used- A set of…

Q: e (2 +y+2) dV, JIIE V + y? + z? where E is the region bounded by the spheres a? + y? + 22 = 1 and r2…

A: ∭e-x2+y2+z2x2+y2+z2dv

Q: wnich of the followi ng functrons is homogeneous? 5x - 12メy ty? Po.) sm xy Ci) eln xy 2

A: To find which of the following function is a homogeneous function. A)fx, y=5x3-12xy+y3B)fx,…

Q: 3) Find The solution of the intigl uglue pablem ty =y+ 3 Vy?+ yl-e) = 2 %3D of the given answers…

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Q: Suppose the temperature at the point (x, y, z) on the sphere x2 + y2 + ?2 = 16 is T= 800xy2z3 .…

A: Solution is given below:

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: (9) Evaluate // 2² + y² + z²)³/? dV where D is the solid region in the first octant between the two…

A: Volume between the two spheres using spherical coordinates

Q: Evaluate //. dV, where E x2 + y² + lines between the spheres x + y + z? and x + y? + z2 = 25 in the…

A: Consider the provided question, Evaluate ∫∫∫E1x2+y2+z2dVwhere, E lines between the sphere x2+y2+z2=1…

Q: 2-By revolving the semicircle: X= r cos t, Y=r sin t, (0<t<n) About the x-axis, Show that the…

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Q: Compute 3xy dS, where S is the surface of the tetrahedron with sides z = 0, y = 0, x + z = 1, and x…

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Q: Evaluate (l. yz dV where E lies above the plane z = 0 and below the plane z = y, and inside the…

A: Given, ∫∫∫EyzdV, Where E lies above the plane z=0 and below the plane z=y and inside the cylinder…

Q: 23. Evaluate II (x² + y? + z²)² dV, where B is the ball with center the origin and radius 5.

A: Given, ∫∫∫Bx2+y2+z22 We know that ρ is 0 to 5 because in spherical coordinates, ρ is the radius.…

Q: Evaluate ez dV where E is enclosed by the paraboloid z = 4 + x? + y², the cylinder x? + y? = 1, and…

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Q: (22. //I (a² + y²) dV where E is the solid that lies between 2 spheres x² + y? + z2 = 4 and a? + y²…

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Q: Evaluate dV, where E is the solid in the first octant bounded by r2 +y? + z2 = 1 E and a2 + y? + z2…

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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 f S S3zdV where E is the solid enclosed by z =1 and z = a? + y? 4 O 27 O

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Q: W hich of the following is not a cylinder? Justify your answer. 4x² - z?= 1

A: Given that , the equation 4x2 - z2= 1 To determine given equations represent a cylinder.

Q: 8. Evaluate ze+y´+z² dV, where E is the portion of the ball centered at E the origin of radius 5, x?…

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Q: 5. Evaluate Sl. x2 dV where is the solid that lies within the cylinder x² + y² = 4 above the plane z…

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Q: 23. Evaluate II (x² + y² + 2²)“ dV, where B is the ball with center the origin and radius 5.

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Q: 5. Use spherical coordinates to evaluate the triple integral ///+y²+²dV, where E is the ball: x? +y?…

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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: 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: 18. Use spherical coordinatcs Evaluate dV,where E is the portion of the unit ball X ty +z²<! that…

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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: The surface area of the solid of revolution generated by rotating 3 x = (y² + 2)ž,1 sys2 about the…

A: Given function is x=13y2+332 where 1≤y≤2. The surface area of revolution of the function is given by…

Q: 1 Evaluate dV, where E lies between the spheres x2 + y2 + z2 = 9 and x2 + y? + z2 x2 + y? + z2 36 in…

A: we want to find the triple integral ∫∫∫E1x2+y2+z2  dVwhere E lies between the sphere x2+y2+z2=9  and…

Q: 1. Evaluate ſf, y dS where S is the portion of the cylinder 4x² + 2y² = 16 that lies between z = 0…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1 I. Evaluate dV, where E lies between the spheres x? + y² + z² = 1 and x2 + y? + z² E x2 + y? + z?…

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Q: Use either form of Green's Theorem to evaluate the following line integral. 03x y dx+ 4x y dy; C is…

A: According to the given information, it is required to find the value of integral using Green’s…

Q: (3) Find The selution of the intigl ualue problem ts =y+ 3 Vy?+E, yle) =0 yl-e) 3,-2 %3D of the…

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Q: Evaluate fff(x +y +:' dV, where a is the solid hemisphere (half of the sphere) enclosed by x +y+ =1…

A: Here in the given question, find the integration of the given function:∭Dx2+y2+z232dVWhere Ω is the…

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

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Q: Quertion: Conidee a dihedral Dy= (agbra" =b'=lab)= 1). Give the detxls of your! work.

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Q: 1. Evaluate the integral: SSS, x² + y² + z² dV where D lies above the cone z = spheres x? + y? + z²…

A: Here we have to evaluate the integral value, where D lies above the cone z= √(x2+y2) and between the…

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 /// xe²+y²+z² dV, where E is the portion of the unit ball x2 + y? + z2 < 1 hat lies in the…

A: Given The given integral is ∫∫∫Exex2+y2+z2dV E is the portion of unit ball x2+y2+z2≤1.

Q: 5. Evaluate SS (x² + y²) dV,where E lies between the spheres x2 +y² + z² = 4 and x² + y² + z² = 9

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Q: Evaluate (xr + y² + =³)? dV, where 2 is the solid hemisphere (half of the Ω sphere) enclosed by x +y…

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Q: Use Green’s Theorem to evaluate ∮C squre toot of (1 + x^2)dx + 14x dy, where C is the triangle from…

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Q: 3: Find the surface area of the part of the paraboloid z = and above the first quadrant. 196 - x -y…

A: The surface area of paraboloid is defined as the sum of the area of all the faces of paraboloid. it…

Q: 1 9. Evaluate dV;where E is the solid between the spheres of radius 1 (x² + y² + z²)³/2 E and 2…

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Q: Evaluate +y² 1 Ez² + y² JJJ₁² dV, where E lies between the spheres z² + y² + 2² +2² 16 in the first…

A: Given that,