Evaluate the integral by changing to spherical coordinates. 16 - x2 32 - x2 - y2 yz dz dy dx x² + 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: Convert the integral from rectangular coordinates to both cylindrical and spherical coordinates, and…

A:

Q: Convert the following integral to spherical coordinates: 8-x²-y² I = dz dy dx -2 J-V4-x² J V æ²+y²

A: We have to convert the given integral to spherical coordinates.

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

A:

Q: Evaluate the cylindrical coordinate integrals

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

Q: A6] Evaluate the integral J: J over the area of a circle of radius 2, using polar coordinates.

A: We have, J=∫∫Ax2y2dxdy   Equation of circle is, x2+y2=22   In polar coordinates, x=rcosθy=rsinθ Here…

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

A:

Q: Evaluate the following integral in spherical coordinates. - (9x2 + 9y2 + 9z²) 3/2 dV; D is a ball of…

A: The solution is given below:

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: V1-x² (1-x²-y² (x² + y? + z²)² dz dy dx -1 J-/1-x2

A: Given ∫-11∫-1-x21-x2∫01-x2-y2x2+y2+z22dzdydx. As it is known that in spherical coordinates,…

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

A: We will use spherical coordinates

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

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Q: Rewrite the following triple integral in spherical coordinates. Do not eval- uate the integral. Show…

A: To rewrite the integral in spherical coordinates ∫-22∫-4-x24-x2∫04-x2-z2x2+y2+z212dydzdx

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: 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

A:

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

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

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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: Change the iterated integrals to spherical coordinates 1 v1-r? /1-x²-y? dzdydx a2+y2+z2 -1 V1-x² -y?…

A: The relation between the cartesian and spherical co-ordinates is given by: x=ρ sinϕ cosθy=ρ sinϕ…

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

A:

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 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: 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: 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…

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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: b) Evaluate the following triple integral by using spherical coordinates. 4 V16-x2 32-x2-y2 I = (3x²…

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

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Q: Evaluate the integral by changing to spherical coordinates. 2-22-y2 ry dz dy dx 0. VI²+y² 0,

A: Consider the provided integral, ∫01 ∫01-x2 ∫x2+y22-x2+y2 xydzdydx Converting to spherical…

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

A: We have given an integral;

Q: V2-x²-y2 f(x, y, z) dz dy dx Let f(x, y, z) =xy Consider the integral,

A: To express the given triple integral in spherical coordinates.

Q: Evaluate the integral by changing to spherical coordinates.

A: Given,

Q: Evaluate the integral by changing to cylindrical coordinates. 100 - y? 10 10 xz dz dx dy x² + y?…

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

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Q: Evaluate the integral by changing to spherical coordinates. 16 – x2 V 32 – x2 - y2 xy dz dy dx x² +…

A:

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: Change the iterated integrals to spherical coordinates 1 y1-z² /1-x2-y2 S V1-z²-y? SS dzdydx…

A: