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

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

A:

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 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…

A:

Q: Use spherical coordinates. ter? + y + z* dV, where E is the portion of the unit ball x2 + y2 + z2 <…

A:

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

A:

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

A: This is a problem of differential Geometry.

Q: Use spherical coordinates to evaluate f (ử+y° +z°)* dydzdx. 3/2

A:

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

A:

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

A:

Q: Use cylindrical coordinates to evaluate d V when

A: The given integral is ∭RxdV where the region R is defined by R:x2+y2≤1, x≥0, y≥0, 0≤z≤2. Converting…

Q: Find the parametric equation of x, y, z where : . z2 = x2 + y2 p. 9 = x2 + y² Nhat is the name of…

A:

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 cylindrical coordinates to valuate fff, z dV where E is enclosed by the paraboloid z = x² + y?…

A: To evaluate ∫∫∫Ez dV E is enclosed by the paraboloid z=x2+y2 and the plane z = 16 z is bounded by r2…

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

A:

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 (6 – x2 - y?) dv, where H is the solid hemisphere x2 + y² + z² <…

A:

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

A:

Q: Find a spherical coordinate equation for the cone Z =Vx² + y2? Select one: а. 4 b. TT 4 С. 4 d. Non…

A:

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

A:

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: Verify that dV = p sin o dp de dy when using spherical coordinates. %3D

A: We have to represent a differential element.

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

A:

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

A: We have to use spherical coordinate to evaluate the triple integral…

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

A:

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. 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: Calculate flw y dV using cylindrical coordinates, x² + y? 0 y > 0, 0 < z < 6.

A: Given:

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: Use spherical coordinates. I/ y2z2 dv, where E lies above the cone o = n/3 and below the sphere p =…

A:

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: Use sine and cosine to parametrize the intersection of the surfaces x² + y² = 16 and z = 4x³. r(t) =

A:

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

A:

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

A:

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

A:

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

A:

Q: Use spherical coordinates. I/| y? dv, where E is the solid hemisphere x2 + y2 + z? s 4, y > 0.…

A:

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

A:

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

A:

Q: Use spherical coordinates. // xex2 + y2 + z? dv, where E is the portion of the unit ball x2 + y2 +…

A:

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

A:

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

A:

Q: c) Use spherical coordinate to evaluate V1-x2 1 Vx2 + y? + 22 dz dy dr.

A: The given problem is to evaluate the given triple integral using spherical coordinates, we have to…

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. 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