1 Usng the eqressions for the volune and area in n-dunensond 2/2 Space givan by Vncr) 11 " and AnG) = 22 %3D requetiualy, shoo that V,G) =1 and A G) =4r

Q: Given that p, = x² +xy, calcultae p, ds, over the region, y <x,0 <x < 1.

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Q: Use špheričal čoördiñatės. Evaluate tet dv, where E is the portion of the unit ball x2 + y² + z² s 1…

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Q: Let Wbe the region bounded by z = 4 – y?, y = x², z = 0. Compute fw x + y+ zdV.

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Q: Show that every positve colufion at Ay + B, k=osl,2 bounded, %3D JK is i-e, osysB-if A<1. 1-A

A: Question: Objective is to find the upper bound of     yk+1=Ayk+B, k=0,1,2,... where yk is positive.

Q: Hiw Enadunte SSS where s is the selid bounded the Śur faces

A: Given - S is the solid bounded by the surfaces x2 + y2 = z2, z = 0, z = 1 To find - Evaluate ∭Sx2 +…

Q: 5. . Find sSSzdv where D is the 2 solid bounded by xty'tz=4 and 2= 13x²+ 3y2. (" sce Cueam Come')

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Q: Fnd the emnd tuber pt e dag emema bedagna ttd be dagn by the thn dent Condtion tar agnal ding y ma…

A: Diagonalization of the Matrix

Q: find the ora of the Region described t vegion bounded by gee"iy=e EIny and

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Q: Let S be the portion of the cylinder z = 1 − x2, in the first octant and between the planes y = 0…

A: The required surface is shown below: Note: If the surface is given by the function z=f(x,y), then,…

Q: 2)Evaluate || dA ,Ris bounded by y = x2 ,y = 1 et2 R. 3)Evaluate | Vy2 + 1dA, Ris bounded by x = 4-…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 18. Ris the annulus in the first and second quadrants bounded by x +y² = 9 and x² + y = 36; 8(x, y)…

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Q: Set up, in either Cartesia over the region within the cylinder x² + y² evaluate the integral. 2م

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Q: 5. If F=2xi - xj + y*k, evaluate ffLF av over the region bounded by the surfaces x = 0, y = 0, y = 6…

A: Given: F→=2xzi∧-xj∧+y2k∧region bounded by the surface x=0,y=0,y=6 and z=x2 ,z=4

Q: Compute integrals b) dz 7 cos(z) ris Countercleckunse oriented rectangle with -2,ス-6,2tースォ Jis…

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Q: 2. Evaluate S SR 72xydA by making appropriate change of variables, where R is the region bounded by…

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Q: Under a change of variables z = u°/3, y = v²/2 , the infinitesimal element of area dædy becomes 6uv…

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Q: ofind the Veelles Such that of A ond R

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Q: and y have density flay)=82y tor Find ECX14) and ECYIX) リフズ7679 %3D

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Q: egral dS over the su 9, where n is th surface element

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Q: 3. Evaluate JS Vr2 + ydA, where R is the region bounded by the circles with center (0,0) and radius…

A: (3) Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: 4. Locate the centroid (x, y)of the following composite areas:

A: The centroid of rectangle is given by x2,y2 where x, y are the length and width respectively. The…

Q: Apply Green's Theorem to evaluate the integral P (4y² dx + 4x² dy) , where C is the triangle bounded…

A: See the details solution in below

Q: Prove that the area bounded by a simple closed curve C is given by | xdy – ydx. Hence, find the area…

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Q: If the region R is bounded between two circles x² + y? = 1, x + = 4, then we have: ev+ dr do dA = +…

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Q: Evaluate SSS z²dV, where R is the region given R by above the plane z=O and between the spheres 2. +…

A: A scalar function is a rule that is used to associate a number, or quantity with a particular point…

Q: Evaluate the double integral || 8xydA, where Dis the triangular region with vertices (0,0), (1,2),…

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Q: 10- Evaluate JJI where E is the region that lies inside the cylinder Vx2 + y?dV E x? + y? = = 16 and…

A: Here we use polar coordinate and Jacobian .

Q: Compute ff 24xyd A where R is the region bounded by R x = 1, x = 2, y = x, y = x².

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Q: need help with 9.2.5

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Q: Jraen fusk hon conespaaday to o d'u z ul) = flx). dx² Find the the egualido for conespoodiang to…

A: Given differential equation is d2udx2+u(x)=f(x)                   (1) boundary conditions are…

Q: use Caushy Reman eduntions to Show that ĕ (Z) anal its devivative F(Z) exist eNerywhere and find…

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Q: 7 If D is the region enclosed by y =-, x = 7, and y = 7x. Then %3D ly dA = 1386. D Select one: O…

A: Solution is given below

Q: J uore program Use a soft groping of ality aith motrix copobilities to'find the eligenualves the…

A: For any matrix, A , the eigen values are calculated by solving the equation, det(A-λI)=0 . Here , I…

Q: With integration by parts, J udv · Judv = UV - O True O False

A: Solve the following problem

Q: Evaluate the double integral. 8y2 dA, D is the triangular region with vertices (0, 1), (1, 2), (4,…

A: we have to find given double integral

Q: If the region R is bounded between two circles x2 +y? = 1 and x²+y? = 16 , then we have: J| x²+y?)…

A: Let's find.

Q: The net of a cone consists of three different two-dimensional areas. O True O False

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Q: Let C be a simple closed curve bounding a region Din R2. which of the following are equal to the…

A: Let C be a simple closed curve bounding the region D in R2.  So using Green's-Theorem,

Q: Apply Green's Theorem to evaluate the integral O(6y dx + 6x dy), where C is the triangle bounded by…

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Q: 2. Evaluate , dV, where o= 45 x²y and V is the closed region bounded by the planes 4x + 2y +:=8, x=…

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Q: Prove that the area of the cardioid 3 r = a(1- cose) is , πα?. 2

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Q: (Compute Sc (-3y+ony Sin(3))dxt (5x²-(ye)du Where C is a Simple Clased cUne in the plane oriented…

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Q: use the funda men tal Theorem of Culculus to find the under Curue of 2. y = -xFl0 x between x = 3…

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Q: 3. Given that p, = x + xy, calculate f,p, dS over the region y sx", 0 < x < 1.

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Q: Let D be the portion of z = 2x + 5y inside z? + y? = 1, oriented up, and let %3D F (y, z, –2).…

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Q: he region bounded by the cylinder x2 + y2 = 9 and the planes z=0 and x +z =9 O 243 O 81T 27TT 729TT

A: Follow next step