S S SVET Evaluate the iterated integral Hint: It maybe be easier to use spherical coordinates. 8-x²-y² (x² + y² +2²)³/2 dz dy dr.

Q: 3. Convert the following integral from rectangular coordinates to both cylindrical and spherical…

A: We have given a triple integral ∫-11∫-1-x21-x2∫11+1-x2-y2xdzdydx We have to convert given integral…

Q: A large metal disk with radius of 1 m has been made. The density of the metal disk is given by p(z,…

A: Given A large metal disk with radius of 1m has been made i.e. r=1 and ρx,y=2+6xy and θ=0 to θ=π3

Q: 4 1 Find the area of the region cut from the first quadrant by the curve r = 2(2- sin 20) ² A= (Type…

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Q: Use cylindrical coordinate to evaluate the integral 1-x²-y² [T 2 √x² + y² dz dy dx.

A: By using cylindrical coordinate to evaluate the integral.

Q: Q2) Evaluate each side of Stokes theorem for a portion of sphere :r=2m, e= T/3, 0<¢<a H= 2r cosO…

A: This question is about application of stkoes theorem

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: Convert dzdydx Into an integral of spherical coordinates (6coso p²sinodpdøde psinødpdøde Option 1…

A: We can solve this using spherical coordinates x = p sin(phi) cos(θ) y = p sin(phi) sin(θ) z= pcosϕ

Q: Evaluate the spherical coordinate integral. R | Ne π 2 2 1- cos Ï Ï 0 0 п p²sin o dp do de

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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: 1olud Evaluate dv Whese sü the 2ィz°-9,4z0 2. hemiphere

A: To evaluate : The triple integrals ∭ y2 dV , where S is the solid hemisphere, x2+y2+z2≤9 , y≥0 in…

Q: 3 '9-x2 3+V9-a2-y? 1 dz dy x² + y² x²+y² a C = L7I Fle,0,6) dp dộ do

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Q: Evaluate the spherical coordinate integral 2π π/3 3 S S S 4p² sin dp do de. & 0 seco

A: I=∫02π∫0π/3∫sec⁡ϕ34ρ2sin⁡ϕdρdϕdθUsing the Power Rule∫xndx=xn+1n+1+C

Q: Q1) Evaluate the integral S dx dy using polar coordinate y 2-y

A:

Q: ارو رهجہ 10. Change dz dy dx into spherical coordinates and evaluate the integral. -1 0

A: ∫-11∫01-x2∫01-x2-y2e-x2+y2+z232dz dy dx To Find: Change the given integral into spherical…

Q: Use spherical coordinates to find the volume of the region bounded by the sphere p = 16 cos op and…

A: Solution :-

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

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Q: For the given triple integral, which of the following is the transformed integral in the spherical…

A:

Q: -2x-x² •√√√x² + y² Write the integral 1.S cylindrical coordinates. DO NOT EVALUATE THE INTEGRAL!!! +…

A: Given an integral: To write the integral in cylindrical coordinates.

Q: V.EVALUATION: Given the following scores: 5, 7, 12, 14, 15, 22, 25, 30, 36, 42, 53, 65. Find: 1. Qi…

A: The given data is already in ascending order: 5,7,12,14,15,22,25,30,36,42,53,65 Q1=(n+1)4thterm…

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

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Q: Evaluate the integral S SS zdV by changing to spherical coordinates. E is the solid pictured below.

A:

Q: 4. The upper hemisphere of the unit sphere can be parameterized, using cylindrical coordinates, as…

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Q: c) Use spherical coordinate to evaluate 1-x² 1 Vx2 + y² + 2² dz dy dx. 0,

A: Given : ∫01∫01-x2 ∫13x2+y21x2+y2+z2 dz dy dx Definition: To evaluate with help of spherical…

Q: Question: Change the order of the following integral. Rewrite the integral by changing to…

A:

Q: Let F= . •ff, curl F S S is the hemisphere x² + y² + z² = 1, z ≥ 0, oriented upwards. Use Stokes'…

A: Given: F→=x2eyz, xexz, z2exy, x2+y2+z2=1, z≥0 To find: ∫∫ScurlF→.dS

Q: Use cylindrical or spherical coordinates to evaluate the integral. NOTE: Enter the exact answer.…

A: Volume by triple integral, conversion of cylindrical coordinates

Q: Use cylindrical coordinate to evaluate the integral 9-x² -2 [²³ [²³² ²³² ²³√x² + y² dz dy dz. 0 0 0

A: Given,         ∫03∫09-x2∫02x2+y2dzdydx