Use spherical coordinate to evaluate Vr2 + y? + 22 dz dy dr. 0.

Q: Use spherical coordinates to evaluate /R Vx2 + y² + z² dV , where B is the ball x² + y? + z? < 10 В

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Q: Use spherical coordinates. (2 - x2 - y2) dv, where H is the solid hemisphere x? + y² + z² < 36, z 2…

A: We have to evaluate ∭H2−x2−y2dV, where H is the solid hemisphere x2+y2+z2≤36, z≥0 Changing into…

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: Use spherical coordinate to evaluate V1² + y? + z² dz dy dr.

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Q: Use spherical coordinates to evaluate 2π FT S 2-r r+z 0 (r² +2²) ³/ rdz dr de.

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Q: Find the moving tri hedral of f R CE) = t, 2E> at %3D

A: This is a problem of differential Geometry.

Q: 2² dz dx dy By converting to spherical coordinates, evaluate

A: Given:  ∫02∫04-y2∫x2+y28-x2-y2z2dzdxdy we need to find following integeral by using spherical…

Q: V4-y? '8-x²-y² By converting to spherical coordinates, evaluate 2? dz dx dy.

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Q: Q3// B Verify that dv3p'sin Ddpd@d owhen using spherical coordinate

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Q: Find parametrizations The portion of the hemisphere x2 + y2 + z2 = 10, y&gt;= 0, in the first octant

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Q: Use spherical coordinates. |II (1 - x² - y²) dv, where H is the solid hemisphere x2 + y2 + z? s 25,…

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Q: VI-y? rz²+y? I = f(x, y, z) dz dx dy.

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Q: Find a spherical coordinate equation for the cone z= Vx2 +y?? Select one: a. 4 b. Non of them С. r…

A: Use the spherical coordinates for this cone as in next step.

Q: Use spherical coordinates to evaluate -VE 0 Vx? + y? +z? dz dx dy

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Q: 6. By converting to spherical coordinates, evaluate 22 dz dx dy. 0.

A: triple integral

Q: Determine the area of the surface with parametric equat ions x = 2u?, y = v², z = 2uv, %D 0<u< 3, 0<…

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Q: What Cartesian equation is equivalent to the given parametric equations? Sx (t) = 2 sint ly (t) = 4…

A: x(t)=2 sin t xt2 = sin t  square both side x24 = sin2 t ...............1   Now, y(t)= 4 cos t yt4 =…

Q: Use spherical coordinates. Evaluate I|| y²z? dV, where E lies above the cone o = n/3 and below the…

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

Q: solid that results when R is revolved about the y-axis.

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Q: Use cylindrical coordinates to evaluate V9-x² r9-x²-y² a² dz dy dx -3 J- 9-x² Jo Do not forget to…

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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: Convert the rectangular equation r +2y? + 2? = 42 + 6x to an 4) equation in cylindrical coordinates.…

A: Consider the rectangular equation: x2+2y2+z2=4z+6x. To convert rectangular equation into equation in…

Q: c) Use spherical coordinate to evaluate UTM TM 1²+y? Væ2 + y? + 22 dz dy dx. UTM &UTM

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Q: Q.1 Use cylindrical coordinates to evaluate (x+y )dzdxdy

A: ∫-11∫01-y2∫0xx2+y2dzdxdy =∫-11∫01-y2∫0xdzx2+y2dxdy=∫-11∫01-y2z0xx2+y2dxdy=∫-11∫01-y2xx2+y2dxdy…

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: 2. By changing to cylindrical coordinate, evaluate r1 (V1-x2 c16 L 2+y2x² dzdydx

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Q: Use cylindrical coordinates to calculate : x? + - y dV W : x + y < 25, 0sz<4 SII»(x² + y² ) dV =

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Q: Evaluate y*dV, where E is the solid hemisphere x? + y? + z² 0. E (Hint: spherical coordinates)

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Q: Use spherical coordinates. SIL Evaluate |I| (x² + y2 + z²)² dV, where B is the ball with center the…

A: We need to evaluate the following triple integration ∫∫∫Bx2+y2+z22dV Where, B is the ball with…

Q: Vi-x² 2-x²-y² Change Vr +y² dz dy dx into cylindrical coordinates, then evaluate.

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Q: Evaluate: , S 9-2²-y? x² dz dy da, using cylindrical coordinates. 3 245 243 245 243

A: As we know that the cylindrical coordinates: x=rcosθ;y=rsinθz=z x2+y2=r2 dydx=rdrdθ Given:…

Q: (d) r2 + x? = 9 in cylindrical coordinates (e) pcos(o) = 1 in spherical coordinates %3D

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Q: O Convert this Entegral From rectangular Coordinate to Spherical Coordina tes (Donot eval vate the…

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

Q: Find the moment of inertia of the plane area generated by the equations y = 8x³, y = 0, and x = 1…

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

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

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Q: 48. Use spherical coordinates to evaluate y'Vx +y +z dz dx dy

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Q: Write the covariant and the contravarian sor for the parabolic cylindrical coordina

A: Introduction: For n-dimensional space, the quadratic differential form dS2=gijdxidxj is known as the…

Q: By changing to spherical coordinate, evaluate (a) z' Vx² + y² +z² dz dy dx (b) " ST* E x² + y° +z?…

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Q: 它们也称 Use spherical coordinate to evaluate Vr² + y² + z² dz dy dx. 0,

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Q: Use Spherical coordinates to evaluate Cx*+ ya+22)² dV where Bis the B. ball with anter at the ongin…

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Q: Use cylindrical or spherical coordinates to evaluate the integral. 2 cVA-y? cv8-x?_y² z?dzdxdy. A…

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Q: The r in cylindrical coordinates must be positive or zero. O True O False

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Q: Evaluate | xz dz dy dx by changing to spherical coordinates.

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Q: Answer true or false in spherical coordinates X,Y,z J p² sin p

A: Given: Jx,y,zρ,φ,θ=ρ2sinφ As we know that; The cylindrical coordinates; x=ρsinφcosθ,…

Q: Use cylindrical coordinates to calculate : x² + y? dV W : 2² + y? < 9, 0<z< 14 SSIW(æ² + y?) dV =

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Q: Ex6:compute 4Cメッッ) du where: 4(メy)4 メサ by using spherical coordinates system.

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Q: Use spherical coordinates. Evaluate /| y² dV, where E is the solid hemisphere x2 + y² + z² s 9, y 2…

A: first convert x,y,z coordinates into hemispherical coordinates than perform integral  detailed…

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: Use spherical coordinates. Evaluate xex + y2 + 22 dV, where E is the portion of the unit ball x2 +…

A: Consider the given: I=∫∫∫Exex2+y2+z2dVE​ is the portion of unit ball x2+y2+z2 that lies infirst…

Q: Use spherical coordinates. Evaluate y² dV, where E is the solid hemisphere x2 + y² + z² s 9, y 2 0.

A: Given  solid hemi sphere is   ;      x2+y2+z2≥  9   , y ≥0