3. Evaluate the triple integral SSS x²y°z=dV,where E is the rectangular box given by E=

Q: (b) / = xyz dV if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

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Q: 10. (1 – y³) dx + (x³ + e*) dy, Č is the boundary of the region between the circles x² + y² = 4 and…

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Q: The differ en tial equation yʻz + 2y'e* = 0 is (a) linear (b) separable (c) homogeneous (d) exact

A: The given differential equation is: y4x+2y'ex=0

Q: 4. Evaluate S, cos dA where D is the region bounded by D = {(x, y)/ VL < x < v3Ln , 0 < y< x² }.

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A: The general solution for the homogeneous wave equation satisfying…

Q: 3) Find The solution of the intigl uglue pablem ty =y+ 3 Vy?+ yl-e) = 2 %3D of the given answers…

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Q: Verify Green's Theorem by evaluating both integrals y2 dx + x² dy = dA ду for the given path. C:…

A: In this question we can verify the Green's Theorem . i.e, ∫C M dx +Ndy = ∫∫R ∂N∂x-∂M∂ydA .

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Q: check if it is homogeneous and to what degree (3x - cosy)dy t_x' dy =0

A: Find your answer below

Q: E ralu ate the given ヤyle integral: S. x² rin dy dz dx

A: Given that, The integration is, ∫0π∫0x∫0xzx2siny dy dz dx We have to find the value of this…

Q: (c) V9-x² dz dy dx 0 Jo

A: we have to find value of integration

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Q: #1. Evaluate the iterated integrals (a) || (6x?y+4x - y) dx dy -2 (b) y2 x²y dxdy

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Q: 3 The triple integral L (x + 2y – z)dxdydz is equal to

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Q: 3. Evalnate. the.allowing.deuale.integral.by.conver.ting.bo. polar.Cta.r.dinates Co.fxdxdy Anse 3.6.…

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Q: 2. Consider the DE y(4) – 4t²y" + 4y" = 0. (a) Is the DE linear? (b) Is the DE homogeneous? Why? (c)…

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Q: 3. Evalnate. the. fallowing.denble.integrals..by.convecking.bo. Can polar.Caa.r.dinates. ... 2 2…

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Q: 5. Use the result of the previous problem to calculate the area of the hypocycloid z²/3 + y2/3 =…

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Q: Transform the following boundary value problems to integral equations: 4. y" + y = s, y(0) = 1,…

A: Solve the intial value problem, using the Laplace transferom

Q: 1. Evaluate the integral: SSf, xe**+y<+zt dV where B is the portion of the unit ball x² + y² + z² <…

A: Here, the region B is the portion of the unit ball x2+y2+z2≤1 that lies in the first octant.…

Q: please explain it step by step

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Q: (1) Sketch the regions of integration. (a) 3m/2 (b) (r,0)r drdo 3m/4

A: The integrations  (a). ∫-π2π2∫04f(r,θ)rdrdθ(b). ∫3π43π2∫34f(r,θ)rdrdθ We have to sketch the regions…

Q: The value of the triple integral (x² + y )dV where E is the E portion of x + y + z? = 4 with 0 < y,…

A: Solution:-

Q: evaluate the given double integral. ca/2 9. xy cos(a?y)dxdy

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Q: Calculate the value of the double integral 2 c3 5(x'y+ xy' )dædy. Ja=0 Jy-0 O 70 O 210 O 190 O 150

A: Consider the given double integral. ∫x=02∫y=035x2y+xy2dxdy First integrate with respect to y.…

Q: 4. Evaluate fl, cos (2) dA where D is the region bounded by D = {(x, y)/ vLT <x < V3Ln,0 <y< x² }.

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Q: The integral JJI eV 4x2 + 4y² + 4z² dV = mt, where R is the solid hemisphere with x2 + y? + z² < 11…

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Q: Evaluate the integral S (10 – 2z) dS, where S is the part of the surface z = S inside the cylinder…

A: The given surfaces are:z=5-x22-y22and the cylinder is x2+y2=1.This can be plotted as follows.

Q: Evaluate the triple integral. SSS 5x²e" dv I where E is bounded by the parabolic cylinder z = 1 - y²…

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Q: 1. Evaluate ſf, y dS where S is the portion of the cylinder 4x² + 2y² = 16 that lies between z = 0…

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

Q: #1. Evaluate the triple integral xy*av, xy?dV, B where B is given by B = {(x,y,z): 2 <x< 3, -1< y <…

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Q: #2. Evaluate the triple integral x dV, E where E is given by E = {(x, y,z) : z< x < 2z, 0 < y<x+z,…

A: Solve it

Q: And And where What is the produc A C sdR = dxi + dyj + dzk 3 Ã = zi – xj – yk Cya S. Ā.dR of…

A: Ans = 11/2  For detail go through the solution

Q: SI 1 Evaluate the triple integral S dx dy dz xyz 1

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Q: 1. Evaluate the integral: SSS, x² + y² + z² dV where D lies above the cone z = spheres x? + y? + z²…

A: Here we have to evaluate the integral value, where D lies above the cone z= √(x2+y2) and between the…

Q: 4. Evaluate x² dV G where G is a solid that lies in the first octant bounded by x2 + y? = 3z and z =…

A: We have solid G in the first quadrant bounded by x2+y2=3z and z=3 equating the above two equations…

Q: 5. Evaluate SS (x² + y²) dV,where E lies between the spheres x2 +y² + z² = 4 and x² + y² + z² = 9

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Q: b.) xyz dv if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

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Q: 1. Evaluate ſſ, y dS where S is the portion of the cylinder 4x² + 2y² = 16 %3D that lies between z =…

A: Given S is portion of cylinder 4x2+2y2=16 that lies between z=0 and z=7. Parametrize the surface s.…

Q: The value of the triple integral (r + y)dzdydx

A: To evaluate  ∫01∫0x∫0x+y(x+y) dzdydx Formula used ∫dx=x∫xn dx= xn+1n+1∫abf1(x)= f(b)-f(a)

Q: the iterated integral Evalua te 2-y 14-y" (~zdxdz dy 2 0.

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Q: Evaluate the triple integral -p (x + 6y) dV where E is bounded by the parabolic cylinder y = 8x² and…

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Q: 3) Evalnate the iterated integral oy Cer the to palar corrdinate, 2x-x a) hny? dy dx

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

Q: 2. Evaluate the double integral. SSp(x – 2y) dA, D = {(x, y)|1< x< 3, (1+x) < y < 2x} а.

A: As you post multiple question according to guideline I only solve the first one. Please request your…

Q: (1) Sketch the regions of integration. (a) 7/2 Jo r3m/2 (b) (1r, 0)r drdo 3n/4

A: Consider the equation

Q: 1. Evaluate the line integral I = = [v¢4x° + y*) dx + x(2x° + 3y*) dy] around the ellipse x/a? +…

A: The given line integral is, I=∮y4x2+y2dx+x2x2+3y2dy We know the Green's theorem:…

Q: Solve the BVP for the disk (exterior Dirchlet problem) v'u = 0, 1< r <o∞ u (1,0) = sin 0 + cos 20

A: The given function is ∇2u=0 The given condition is u(1,θ)=sinθ+cos 2θ We have to find the general…

Q: Evaluate the triple integral (x + 8y) dV where E is bounded by the parabolic cylinder y = 4x² and…

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Q: If we rotate the region under the curve y = 8 between x = 2 and x = 3 about the x-axis, what answer…

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