(b) f(x, y) dA where D lies below the paraboloid z = x2 + y?, above the ry-plane, and inside the %3D cylinder z2 + y? = 4. %3D

Q: Compute the triple integral and please show work

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Q: xxS y dS S is the part of the paraboloid y= x 2 + z2 that lies inside the cylinder x 2 + z2 =4

A: And the projection of S onto the xz-plane is given by the disk So using the parameterization in x…

Q: Transform the equation rydx – (z+2) dy = 0 into the form of a %3D variable separable f(z) dz + g(y)…

A: Here, the given differntial equation is: xy dx-(x+2)dy=0...(1) To write the eqaution in form of f(x)…

Q: 1. Let E be the solid under the paraboloid 2=r'+y. above the ry-plane, and inside the cylinder +y =…

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Q: Evaluate J₁ 1 E x² + y² + z² x² + y² +2²= 25 in the first octant. dV, where E lies between the…

A: Here we need to use spherical co ordinate system to find value of integral  Relation between…

Q: 8.Evaluate the triple Integral. Te by The paraboloid X=2yt + 2z? and the plane X=2. 7x dV, where E…

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Q: Q) S = the part of the paraboloid z = 10-x^2-y^2 above z = 1 F = [x^3, xy, z] Find the flux of F…

A: Step:-1 Given that S is part of paraboloid z=10-x2-y2 above z=1 Since, given that z=10-x2-y2 and…

Q: Consider the PDE y Ur + a Uyy + Uz – Uy = r² + y? In what region of the xy-plane is this PDE…

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Q: evaluate both the line integral and the double integral. 16. P(x, y) = 2x – x³y°, Q(x, y) = x³y°, C…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 2 + x² + y°, the cylinder z² + y² = 2, and…

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Q: 4. Where does the curve r(t) = ti + t²j+ (3 t2)k intersect the paraboloid z = x2 +y² ?

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Q: The solid that is the common interior below the sphere x² + y2 + z2 = 80 and above the paraboloid z…

A: Given sphere is x2+y2+z2=80and the paraboloid z=12x2+y2set up a triple integral for the volume of…

Q: (b) 6xy dV, where E lies under the plane z=1+x+y and above the region in the xy-plane bounded by the…

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

Q: a) Evaluate (-ri-yj+2z k) n dS, where a is the portion of the paraboloid : 3x +3y between the planes…

A: We have to Evaluate the Integral using polar coordinate

Q: Evaluate ffS. Vx² + y² dV, where E is the region tha lies inside the cylinder x? + y² = 16 and…

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Q: Find F. dr, where F(x, y) = (xy² + cos x)i+(x²y+sin y)j and C is the ellipse C x2 + 2y2 = 9,…

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Q: 2. Evaluate the triple in tegral where E is the y-2x2+2z20nd the plane y= 8. solid bounded by SI…

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Q: Find the centroid of the boomerang-shaped region between the parabolas y2 = -4(x - 1) and y2 = -2(x…

A: Parabolas are

Q: (2) Use the transformaiton u = xy, v = x² – y? to find JJ (æ* – y*)e*³ dA where R is the region in…

A: Given: The region bounded by the hyperbola xy=1 &3, x2-y2=3 &4 Where u=xy and v=x2-y2

Q: Evaluate ez dV where E is enclosed by the paraboloid z = 4 + x? + y², the cylinder x? + y? = 1, and…

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Q: Consider the PDE Y Urr + x Uyy + Ux – Uy x² + y? In what region of the xy- plane is this PDE…

A: compare the given equation with Auxx+Buxy+Cuyy+Dux+Euy+Fu=G A=y,B=0,C=x,D=1,E=-1 calculate B2-4AC…

Q: 4. Evaluate III #V 1 √x² + y² dv G where G is a solid that lies inside the cylinder x² + (y-2)² = 4,…

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Q: Evaluate /|/. x dV where E is the solid enclosed by the paraboloid x = y²+z² and the plane x = 9

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Q: Evaluate // e² dV where E is enclosed by the paraboloid z = 2 + x² + y², the cylinder E x² + y? = 3,…

A: Since we are given with the multiple number of questions and answered according to the guideline.

Q: C is the intersection curve between the paraboloid z=x²+y² and

A: Given that C is the intersection curve between the paraboloid z=x2+y2 and the cylinder x2+y2=1.

Q: • SSS ²³² x² + y² = 2, and the xy plane. Evaluate e² dV where E is enclosed by the paraboloid z = 6…

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Q: (d) The 2nd order PDE uzz +r Uyy = 0 is hyperbolic if: (A) x20 %3D (B) r >0 (C) z< 0 (D) z<0

A: Given PDE is uxx + xuyy = 0

Q: Find F.dS if F (x, y, z) = 2xi+2yj+2zk and S is t he part of the paraboloid z = 8-x²–-y? lying above…

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Q: (8) Find the point(s) where the line r(t) = ti+(1+t)j+5k intersects the paraboloid z = x² + y?.

A: A detailed solution is given below.

Q: 2. Evaluate ([.(Vx F). ds, where S is the surface of the paraboloid x2 + y2 + z = 4 above the…

A: We have given F→=(x2+y-4)i+3xyj+(2xz+z2)ksurface is given x2+y2+z=4 and above the xy planediagram of…

Q: Consider the PDE y u + Uyy + u, - Uy = 2 +y? In what region of the xy-plane is this PDE elliptic? xy…

A: The objective is to find in what region of the xy-plane the pde is elliptic.

Q: At what points does the curve r(t) = ti + (3t - t2)k intersect the paraboloid z = x2 + y2? (If an…

A: Given- r(t)=ti^+(3t-t2)k^z=x2+y2 To find the intersection point of the given curve and paraboloid.

Q: 11. Evaluate ([(y+z³ )dS where S is the part of the paraboloid x = 4- y – z² that lies in front of…

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Q: Find the value of ∫∫s(x^2y^2z^2)dS correct to four decimal places, where S is the part of the…

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Q: (b) || 6xy dV, where E lies under the plane z 1+x + y and above the region in the xy-plane bounded…

A: A triple integral involves the integral with respect to x,y, and z. In this problem, we have to…

Q: Evaluate 1 dv √x² + G where G is a solid that lies inside the cylinder x² + (y − 2)² = 4, above the…

A: Please see the attachment

Q: Evaluate € fff.₂²². e² dV where E is enclosed by the paraboloid z = 3 + z² + y², the cylinder z² +…

A: We need to find integral.

Q: Evaluate the triple integral.  (x2 + y2) dx dy dz; W is the pyramid with top vertex at (0, 0, 2)…

A: The given triple integral is,

Q: Find y dV, where E is the solid bounded by the parabolic cylinder z = = 2 and the planes y = 0 E and…

A: The solution is given below

Q: Evaluate e dV where E is enclosed by the paraboloid z = 2 + x² + y², the cylinder æ? + y² = 5, and…

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Q: Is it true or false that by using a suitable translation x = x' + xo, Y = y' + Yo, it is possible to…

A: Transforming the conic equation

Q: At what points does the curve r(t) = ti + (6t – t2)k intersect the paraboloid z = x² + y2? (If an…

A: Given, r(t)=t i +(6t - t2)k ......(1) and z=x2+y2 .......(2)

Q: Example 6: Evaluate ez dz dy dx E Where E is enclosed by the paraboloid Z = 3+ x? + y² , the…

A: The given problem is to evaluate the given triple integral of given function ez for which region E…

Q: (b) Find the surface area of the portion of the paraboloid z-2-x -y above the xy- plane. AMINATION A…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 4 + x² + y², the %3D cylinder x? + y² = 3,…

A: We need to evaluate integral.

Q: 11. Evaluate ([(y² +z? )dS where S is the part of the paraboloid x=4-y -? that lies in front of the…

A: We will evaluate the given integral.

Q: calculate ∫ ∫ ∫Ty dv, being the T region inside the paraboloid z= 1/(x2+y2)the sphere x2+y2+z2=5

A: We need to calculate the triple integral ∫ ∫ ∫Ty dv, where T being the region inside the paraboloid…

Q: Use Cartesian coordinates to evaluate y² dV D where D is the tetrahedron in the first octant bounded…

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Q: a) Evaluate //(-ri-yj+2: k) n dS, where a is the portion of the paraboloid : = 3r - 3y between the…

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