VI-x? (/2-x²-y² S xy dz dy dx 0 Jo Vx²+y²

Q: (c) Write the integral 3 2 + hpæpzp z + „h in spherical coordinates. Do not evaluate the integral.

A: We will find out the required solution.

Q: Change the iterated integrals to spherical coordinates 1 V1-x V1-x²-y x² +y²+z? 0 -V1-x? -V1-x²-y² |

A: The cartesian coordinates can be converted to spherical coordinates by using the formula…

Q: 3 LL -3√√√9-x² Jo √9-x²-y² (x² + y² + z²) dz dy dx

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Q: Find using spherical coordinates integration zVz? + x² + y²dzdydx VA-x² Jo

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Q: 43, 44, and 45 Evaluate the integral by changing to spherical coordinates. 43. xy dz dy dr

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Q: Evaluate the cylindrical coordinate integrals

A: To evaluate: ∫02π∫0θ/2π∫03+24r2  dz r dr dθ

Q: Evaluate the following integral using spherical coordinates: Z 1 0 Z p1 −x2 0 Z p2 −x2 −y2 px2+y2 z…

A: Consider the given integral, ∫01∫01-x2∫x2+y22-x2-y2z2dzdydx now,change the rectangular coordinates…

Q: a²-y² •Va²-x²–y² а (2²z + y²z+ z*)dzdxdy. Va²-y? -Va²-x²-y² a |

A:

Q: 1 Let f(x, y, z) =xy• Consider the integral, f(x, y, z) dz dy dx

A:

Q: Evaluate the integral by changing to spherical coordinates. (x³ + xy² + æz²) dz dy dæ

A: The limits of integration are  -1-x2-y2≤z≤1-x2-y2, 0≤y≤1-x2 and -1≤x≤0 It is one-fourth of the unit…

Q: Evaluate the following integral using spherical coordinates: [ z dz dy dr. 0

A: Given problem:-

Q: Change the iterated integrals to spherical coordinates 1 1-? V1-1² y? z²+y²+z2 dzdydz…

A: We will use spherical coordinates

Q: Evaluate the integral below by changing to spherical coordinates. 81 - y V 81 – x2 - y2 (x²z + y?z +…

A: We have to solve the given intregal

Q: Evaluate the following triple integral by changing to spherical coordinates. LI T (a + y° +…

A: Here we use the sphere coordinate to find the volume of solid.

Q: Evaluate the integral by changing to spherical coordinates. 2 - x2 -y2 16 x2 4 yz dz dy dx 0 10 x2…

A: The integral is given by,

Q: Convert the integral to spherical coordinates and evaluate it. 5 V 25-x2 5+/25–x²-y² y² + z² dz dy…

A: The limits of integration in the rectangular coordinates are   -5≤x≤5, -25-x2≤y≤25-x2,…

Q: Evaluate the following triple integral by changing to spherical coordinates. 8-x2-y2 (r² + y? + 2?…

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Q: Evaluate the spherical coordinate integral. So Jo e sin p do do d0 O 10 20 3. O 10r 20 3

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Q: 12. Change the Cartesian integral to an equivalent polar integral dy dx re-r dr d0 re-p? -JT re-r dr…

A: In this question we have to convert the integral to an polar integral.

Q: Evaluate the integral below by changing to spherical coordinates. V 25 – y? ,V 25 – x² – y? 25 – x2…

A: The triple integral of a function f taken over the sphere x2 + y2 + z2 = a2 is of the form:

Q: Evaluate the following integral by first converting to an integral in cylindrical coordinates. 3xz?…

A: Here we have to evaluate the given integral by converting to cylindrical coordinates.

Q: Evaluate the integral by changing to spherical coordinates. 6 V 36 - x2 72 - x2 - y2 xy dz dy dx

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Q: Evaluate the integral by changing to cylindrical coordinates: , N Sy xzdzdxdy x²+y²

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Q: Evaluate the following integral in spherical coordinates. S. 1/2 TI|+y? +z2) dv; D is the unit ball…

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Q: Evaluate the integral by changing to spherical coordinates. VI-z 2-1²- ry dz dy dr = Vz²+

A:

Q: Evaluate the integral below by changing to spherical coordinates. 81 81 x2 - y2 (x²z + y?z + z³ ) dz…

A: The given problem is to evaluate the given triple integral by converting the integrals from…

Q: Evaluate the following integral using spherical coordinates: /25-12-y2 ? dz dy dr. 01

A: The given integral is, ∫-55∫025-x2∫025-x2-y2z2dzdydx.…

Q: Evaluate the spherical coordinate integral. 3 sin o o2 sin ø do do de 3n2 9T2 972 277 8.

A: we have to evaluate the spherical coordinate integral

Q: Evaluate the integral by changing to cylindrical coordinates. 49 - у? xz dz dx dy x² + y2 49 - у?

A:

Q: Evaluate the following integral in spherical coordinates. - (x² + y2 + z2) 3/2 dV; D is a ball of…

A: Given: ∭De-x2+y2+z232dV, where D is a ball of radius 7. To find: Equivalent triple integral using…

Q: 5. Use spherical coordinates to evaluate the integral , z dV where E is the region between the…

A:

Q: Change the iterated integrals to spherical coordinates dzdyda 0 0

A: We have to change the given integral into spherical coordinates.…

Q: Change the iterated integrals to spherical coordinates 1 V1-z VI-z²_y² 7+y²+z? dzdydx -1-Vi-z-Vī…

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Q: Set up the iterated integral in cylindrical coordinates to find the moment of inertia (BUT DO NOT…

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Q: Va²-y? Va²–x² -y? ra (x²z+ y²z+ z*)dzdædy. Va²-y? Va2-x2-y2 а | |

A:

Q: Convert the integral from rectangular coordinates to both cylindrical and spherical coordinates, and…

A: Given: ∫07∫049-x2∫049-x2-y2x2+y2+z2 dz dy dx Now we have to convert into cylindrical coordinates and…

Q: Evaluate the integral 1 V1-y² V2-x²– y² (x² + y? + 2?) dzdxdy 2+y² by changing it to spherical…

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Q: 5. Evaluate the following integral using spherical coordinates: 2-x²-y² ста z dz dy dx. x² + y²

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Q: (b) Evaluate the following triple integral by using spherical coordinates. 16-x2 32–x²-y2 I = (3x² +…

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Q: Evaluate the following integral in spherical coordinates. 3/2 JII?+y² +z?) dv; D is the unit ball D…

A: According to question, Given integral, ∫∫∫D x2 + y2 + z2 32dV where, D = unit ball.

Q: Evaluate the integral by changing to cylindrical coordinates. 25–1² r25-r² –y? V? + y dz dy dr

A:

Q: Evaluate the following integral using spherical coordinates: 18-a²-y² 2*dz dy dx. 1²+y²

A: here firstly we find region it help in finding the limit of integration in polar coordinates.

Q: Evaluate the following integral by first changing to spherical coordinates. V4 z dz dx dy -2 Jo

A: Here we have to evaluate the given integral by first changing to spherical coordinates.

Q: Evaluate the following integral in spherical coordinates. SII+ +2) 17/2 dV; D is the unit ball D…

A: Integral in spherical coordinates

Q: Convert the integral below to cylindrical coordinates and then evaluate the integral. Exact answers…

A: Convert the given integral              I=∫01∫01-x2∫14-x2+y2xyx2+y232dz dy dx into cylindrical…

Q: Evaluate the following triple integral by changing to spherical coordinates. 8-x² –y² LL V4-x2 (x² +…

A: