Convert the given integral to spherical coordinates where S is the solid that is bounded below by the xy-plane, and bounded above by the sphere x² + y² + z² = 1. O A. O B. O C. O D. II S (x² + y²)dv 2π [²[*['p² sin² #dpdøde 70 0 270 [²[*p¹ sin³ $dpdøds 2π [²* [*['p² sin³ #deded+ 2π [*[['p² sin² #dedøde

Q: Find the area of the region bounded by the closed parametric curve = 5 sin t-2 cos t, y = 6 sin t+6…

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

A: The given problem is to evaluate the given triple integral using spherical coordinates, We have to…

Q: Consider the plot of the solid r = 1 + Sin[a*phi]*Sin[b*theta]] in a spherical coordinate system.…

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

A: This question is about application of Stokes theorem

Q: A) J. J. J,2-2rainb, rcose dzdrde ,2 x dzdrdy to cylin- If we change the integral SS drical…

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Q: (x, y, :) (p, 0, ) p² sin(o [Practice] Demonstrate the fact that the Jacobian when we convert from…

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Q: Find the area of the plane z = 4x + 3y for all (r, y) E R where R is the region in the first…

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Q: Which of (a)–(c) is the equation of the cylinder of radius R in spherical coordinates? Refer to…

A: According to the given information it is required to write the equation of the given cylinder 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: (a) For what value of n does V· (r2nêr) = 0? (b) For what value of n does V x (r2nêr) = 0? %3D

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Q: (c) Evaluate zdz dy dr using spherical coordinates.

A: Triple integral is used to integrate the function of three variable over the three-dimensional…

Q: 3. Verify Stokes' Theorem for fas F. dr, where F = −yx²i + xy²j + zk, and S is the part of the…

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Q: Which of the following represents the equation z=x2+y2 in cylindrical coordinates?     r2=z…

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Q: V-cot? u +4cot u –1 du = ? integralini hesaplayınız. sin?

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

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Q: Use spherical coordinates. Evaluate SSS √x² + y² + z² dv, where E lies above the cone z = √x² +1 and…

A: The equation of the cone is z=x2+y2. The equations of the sphere are x2+y2+z2=1 and x2+y2+z2=4. We…

Q: Use spherical coordinates to evaluate fff (9-x² - y2) dV where E is the solid hemisphere E x² + y2 +…

A: To Evaluate: The integral ∫∫∫E9-x2-y2dV where E: x2+y2+z2≤9 , z≥0 using spherical coordinate system.

Q: 20.Evaluate The intcaral below by changing to spherical coordinates. 100-4 100-x-4 10 -10

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Q: Convert 18-22-y2 22 +y? +z dz dz dy into spherical coordinates. Hence evaluate the integral.

A: The volume of a solid can be calculated using the triple integrals in the spherical coordinates. The…

Q: /16–y² /32–2²-y² n[L 2² + y* + z®)dzdzdy in nvert 1²+y² •1/2 4/2 -/2 Jo п/2 " T p* sin ódpdődý •4/2…

A: from the integral limits are as  follows 0 ≤ x ≤ 16-y2 0 ≤ y ≤ 4  x2+y2 ≤ z ≤ 32-x2-y2

Q: 14. ƒƒƒÂ(x² + y² + z²) dV, where D is the solid region inside the sphere p = 2 cos & and outside the…

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Q: Show that in spherical coordinates: 5 ( 2 ) + 50 ²7 (20) V = er + eo [] 1 rsin 8 do

A: In spherical coordinate system, We have to Show: ∇→=er→∂∂r+eθ→1r∂∂θ+eϕ→1rsinθ∂∂ϕ.