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

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

A:

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

A:

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: |Evaluate the following iterated integral by changing to cylindrical or spherical coordinates as is…

A:

Q: When converting the triple integral to spherical coordinates, it becomes of the form V9-x² -y² vターx。…

A:

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

A: Given problem:-

Q: Convert the following integral into a triple integral in spherical coordinates: /9-y² 18-x²-y² (x² +…

A:

Q: SS S y=0 x=y z= arctan(²) dzdxdy =

A: The given problem is to convert the given triple integral in Cartesian coordinates to triple…

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

A: To convert the integral to both cylindrical and spherical coordinates, and to evaluate one of them.…

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

A:

Q: Change the iterated integrals to spherical coordinates 1 VI-x VI-x-y? x²-y? 1 dzdydx x2 + y2 + z2 -1…

A:

Q: Convert the given iterated integral from Cartesian coordinates to spherical coordinates. -1 4-x2-y2…

A:

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: 10 Evaluate the following integral by first converting to an integral in spherical coordinates. 18y…

A:

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

A:

Q: Convert the following iterated integral to cylindrical coordinates: Vx2 + y? dzdydx. 0.

A:

Q: |Evaluate the following iterated integral by changing to cylindrical or spherical coordinates as is…

A:

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

A:

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 integral below by changing to spherical coordinates. 4 - y2 4 - x2 - y2 x?z+ y²z+ z³)…

A:

Q: Evaluate the following triple integral by changing to spherical coordinates. 8-2-y? (1² + y² +…

A:

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 integral by changing to spherical coordinates. 36- х2 V 72 - х2 - у2 yz dz dy dx x² +…

A: According to question given that∫06∫036-x2∫x2+y272-x2-y2yz dz dy dx

Q: Rewrite the given triple integral in cylindrical and spherical coordinates and evaluate one of them…

A: Given integral ∫−22∫04−y2∫−4−x2−y24−x2−y2zx2+y2+z2dzdxdy

Q: Evaluate the following triple integral by changing to spherical coordinates. /8-x²-y² (1² + y² +…

A:

Q: Change the iterated integrals to spherical coordinates 1 I- VI-a-y? a² +y? +z dzdyda -1 " S p sin o…

A:

Q: 1-z z dz dy dr V1-z 3x2+3y2

A: Triple integral is used to integrate functions of three variables over a three-dimensional region.…

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

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

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…

A:

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

A:

Q: Convert the following integral to spherical coordinates and evaluate the integral. 1 Ni- NIA dy de…

A:

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

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 integral by changing to spherical coordinates.

A: Given,

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 integral by changing to spherical coordinates. 10 200 – x2 – y2 V 100 – x2 xy dz dy dx…

A:

Q: Convert the following iterated integral to cylindrical coordinates: LL VF+yi dzdydx.

A:

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: