5. Use spherical coordinates to evaluate r2+ y2 +22 dz dy dr. 16-

Q: (c) dz dy dx

A: Let's find.

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: Find an equation of the form p = f(0, $) in spherical coordinates for the surface z3 = 4(x2 + y2)…

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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: b.) √4-1²-² √3x²+3y² TEN nates. z dz dy dx from Cartesian coordinates to spherical coordi-

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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: 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: 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: T 27 Convert ( 5, from 3 spherical to cylindrical coordinates -5V3 ㅠ 5 5V3 5/3 7 5 4 2 (등급) 5V3 T 2…

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

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Q: In changing variables to spherical coordinates, the dV in I| f(x, y, z) dV becomes p cos o dp do de.…

A: By using formulaes for change of integral from Cartesian to spherical

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

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Q: 5. Use spherical coordinates to evaluate /16--2² Not √16¬x² / √x² +yª √x² + y² + z² dz dy dr.

A: The given problem is to evaluate the given triple integral by converting the Cartesian coordinates…

Q: the LLE + y² + z*)% dzdydx 2n n 3 to spherical coordinates becomes the form TI sin(4)dpdød® True…

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Q: (a) Express the following points in cylindrical and spherical coordinates: (i) P(1, -4, -3); and…

A: We need to find cylindrical and spherical coordinates.

Q: 2. By changing to cylindrical coordinates, evaluate 2 2π Stt. [²* * cos p² sin³ o dp do dô 0

A: To Evaluate: The integral ∫02π∫0π/4∫02/cosϕρ4sin3ϕ dρdϕdθ by converting it to cylindrical…

Q: Use spherical coordinates. Evaluate (6 – x2 - y?) dv, where H is the solid hemisphere x2 + y² + z² <…

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Q: By transforming into spherical polar coordinates, evaluate JJ) 1-x². ff - (- dxdydz , taken…

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

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Q: Find an equation of the form z = f (r, θ ) in cylindrical coordinates for z^2 = x^2 − y^2.

A: z2=x2-y2

Q: In changing variables to spherical coordinates, the dV in J f(x, y, z) dV becomes p² cos o dp do do.

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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: find an equation of the form ρ = f (θ , φ) in spherical coordinates for the following surfaces  z =…

A: To convert z=x2+y2, in spherical coordinates, substitute z with ρ cosϕ, x with ρ sinφ cosθ and y…

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

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Q: Let N be the lower hemisphere of the sphere of radius 5 and let H • Construct dS for 2. Try using…

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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: Exercise 2 Use spherical coordinates to evaluate f[[(9-x² - y³ ) dV , where E is the solid…

A: Introduction: When we perform a triple integral over a spherical region, it is convenient to follow…

Q: 1) Use spherical coordinates to evaluate 4-y² c4-x²-y² 4-x2-y2 Li L y²/x² + y² + z² dzdxdy

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Q: (a) Express the following points in cylindrical and spherical coordinates: (i) P(l, -4, -3); and…

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Q: Evaluate the spherical coordinate integ A1 8 sin o | ? sin d dp dɖp de do de 0 0 512 2 O A. -

A: Here we have to calculate I= ∫0π∫0π∫08 sinϕ ρ2 sinϕ dρ dϕ dθ

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

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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: 3. Use spherical coordinates to valuate ff, y? dV where E is enclosed by the hemisphere x? + y? + z?…

A: Given that  ∫∫∫Ey2dV and  enclosed by the hemisphere, x2+y2+z2≤9,y≥0 Here to evaluate the integral,…

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 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: 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: onvert T (=² + y² + z®) dzdzdy into spherical coordinates. /4 /3 /2 2/2 - 2×/3 /2 -2/2 /4 /2 2/2 /2…

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Q: (b) To change from spherical coordinates to Cartesian coordinates we use the equations x =r cos 0, y…

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Q: Find an equation of the form p = f(0, $) in spherical coordinates for the surface. x2 - y2 = 36 p =…

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Q: c) Use spherical coordinate to evaluate x dz dy dr 4-x²-y²

A: Sketch the region and find range of variable

Q: 5. Use spherical coordinates to evaluate [[[ (x² + y² + 2²) ² dv D where D is the solid hemisphere…

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

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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: Evaluate the spherical coordinate integral. 7/2 7/3 8 sec 8 sec o Q sin o cos o do do de 5 sec o

A: We have to find the value of given integral.

Q: 5. Use spherical coordinates to evaluate LIVE √√= ²+ y² + 2² dz dy dr.

A: Given ∫-44∫-16-x216-x2∫x2+y24x2+y2+z2 dzdydx

Q: Use spherical coordinates. Evaluate TI (x2 + y2 + z²)² dv, where B is the ball with center the…

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