S* ds. x* + y+z*= x+y - Evaluate where S is the part of the sphere that lies above the cone

Q: 2. Use Green's Theorem (and only Green's Theorem) to evaluate |(2? + y)dx + (x² – y³)dy, where C is…

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Q: Evaluate ||E y²z² dV, where E lies above the cone o and below the sphere p = 1. = T/3

A: Given, ∫∫∫Ey2z2dV   ....(i)Let x=ρsinϕcosθ y=ρsinϕsinθ and z=ρcosϕAnd we know…

Q: Calculate the surface area of the following: the cap cut from the sphere r² + y² + z² = 3 by the…

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Q: Let q (1) = . a. Where does q) intersect with the sphere x + y² +z? = 5? b. Find q'(t) and q'(n). c.…

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Q: Evaluate [[ (x + y? +=?)2 dV, where 2 is the solid hemisphere (half of the sphere) enclosed by x +…

A: Change the given system to a spherical coordinate system and solve it.

Q: 28. F(x, y, z) = x³i+y°j+z°k, and S is the sphere of radius 3 and centered at the origin.

A: divF→=ddxx3+ddyy3+ddzz3        =3x2+3y2+3z2        =3x2+y2+z2  by divergence theorem,…

Q: Find the surface area of the part of the sphere x2+y2+z2=49 that lies above the cone z=(x2+y2)1/2

A: Consider the provided question,

Q: Ex.7 The area of the surface ∑ = {(x,y,z) €R® : (x² + ²) < 1, z = 9 + xy} is: (A) - 5 (B) 4개 2 (C)…

A: Using polar coordinates.

Q: Evaluate [f[(x² +y² +=?)2 dV, where 2 is the solid hemispi sphere) enclosed by x +y +z =1 and above…

A: We have to choose the correct answer from the given options

Q: Integrate H(x, y, z) = yz, over the part of the sphere x2 + y2 + z2 = 4 that lies above the cone z =…

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Q: 4 The area of the surface S = {(x, y, z) E R³ : z = 5 – z2 – y², z > 3} equals (A) 47 (B) 13 (C) (D)…

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Q: 2. The solid outside the cylinder x² + y² = 1 that is bounded above by the sphere x² + y? + x? = 8…

A: The solution is given below

Q: Find the point on the sphere x +y +z = 4 that is close O A. V11 V11 9. V11 (유 O B. 11 V11 V11

A: Solution of the problem as follows

Q: Evaluate E where E is the region above the cone y = and below the sphere x2 + y? + z² = 1.

A: The triple integral can be obtained using the formula…

Q: Which one of the following surfaces is the aph of f(z, y) = y -2 ? 3..

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Q: Find the surface area of the portion of the sphere x2 + y2 + z2 = 25 inside the cylinder x2 + y2 =…

A: Recall:  The formula of surface area is S=∫∫S1+∂z∂x2+∂z∂y2 dA

Q: 2. Evaluate f Ss²dS, where S is the unit sphere x2 + y² + z² = 1.

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Q: Find the surface area of a sphere with radius, r=8 in. S.A. = in (Type an exact answer in terms of…

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Q: The area of the surface p = 2, 0sz<5,0<¢< T is 201 Select one: O True O False

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Q: 17. Evaluate the integral: S, 9x? – 6dx. 18.Determine the center of the circle x² +y² = 25. %3D

A: (17)  Given that I=∫-159x2-6 dx It is known that ∫xndx=xn+1n+1 So, I=9x33-6x-15 =3x3-6x-15 Now we…

Q: Let B be the ball with center at the origin and radius 1 3(x² + y + z?)dV = %3D B

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Q: Find the olume of the solid cut Prom the sphere 8=2C@SQ by the Cone Z= Jx+ ý Ans/ T

A: The given question is related with triple integral. We have to find the volume of the solid cut from…

Q: 8. Evaluate ze+y´+z² dV, where E is the portion of the ball centered at E the origin of radius 5, x?…

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Q: Use geometry to evaluate ∫∫∫R 1 dV where R is the region inside the sphere x2+y2+z2=4.

A: Given R as the region inside the sphere

Q: 7. If F = (yz,-2xz,xy), the value of ||F.n dS , where S is a sphere of radius a centered at the…

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Q: Describe in words the region in R' represented by the equation x² + y² + 2y + z² < 3 A plane. A…

A: The given equation is x2+y2+2y+z2≤3. We have to describe the given equation in words.

Q: - 2 and Evaluate || curl(F)·dS where S is the portion of the top half of the sphere x +y +z? = 4…

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Q: Find the center and radius of circle x“ + y° - 2x-4y+1=0. Prove thot (0

A: I am solving question 1. if you want other question to be solved then repost.

Q: ind the exact area of the surface obtained bY rotaing -- 2)2, 2sys3

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Q: Let B be the ball with center at the origin and radius 1 I//3(x² + y + z?)dV =

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Q: 10. Using Stoke's theorem, evaluate y dx+ xz dy+x² dz where C is the boundary of the triangle cut…

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Q: 3. Evaluate ox?y dx + xy? dy using Green's y 2 Theorem, where C is positively oriented by line y =x…

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Q: 9. Using Stoke's Theorem Evaluate [(2x – y)dx – yz dy – y zdz) where c is the circle x +y =1,…

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Q: 4 The area of the surface S = {(x, y, z) € R³ : z — 5 — z² - y², z ≥ 3} equals (A) 4T (B) (C) (D)…

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Q: 22. Evaluate xyz dV, where E lies between the spheres p - 2 and p- 4 and above the cone - 7/3.

A: Solution:-

Q: 12- Evaluate JJI (x2 + y? + z?)dvwhere B is a ball with center the origin and radius 5. B

A: Given problem is :

Q: Evaluate ∬S(x2+y2)dS, where S is the surface z=4−x, 0≤x≤2, 0≤y≤2.

A: Given z=4-x , 0≤x≤2 ,0≤y≤2 to evaluate ∬Sx2+y2dS where S is surface

Q: EX. Find the volune of the solid region lymg mside both the sphere Xtuf+2?= 402 and the cylmeder…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Evaluate [[[(x² + y² +=?)2 dV, where 2 is the solid hemisphere (half of the Ω sphere) enclosed by x…

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Q: Use spheri\cal coordinatcs Evaluate y'zdV, where E lies above the cone 4 = /3 and below the Sphere…

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Q: Describe in words the region in R° represented by the equation x? + y² + z² > 4 A A point R A…

A: The given equation is x2+y2+z2≥4. We have to describe the given equation in words.

Q: Evaluate ||| Vx² + y² + ²²&V where S lies above the cone z = Vx² +y° and between the spheres x + y…

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Q: Find the area of the portion of the sphere x2 + y² + inder x2 + y? = 6y. %3D

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Q: H.w/ Findthe forthes tand closest paints.ah the sphere x+y+2'=36 from p(l2,2).

A: I used Lagrange Multiplier to solve this.

Q: (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 35. Above the cone z = a² + j? and below the sphere x² + y² + z² = 1

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Q: The radius of the sphere x2+y2+z2+2x-2z-14=0 is r= (Round your answer correct to three decimal…

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Q: Let S be the sphere x + y² + z? = 9 oriented outwards, and F = (5x, 7z, –3y). Evaluate: F. dS. The…

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Q: 1) A) Find the area of the portion of the sphere x? + y + =9 lying inside the cylinder x2 + y? = 3y.

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