Evaluate [ ( (x2+ yz) dV, where R is the rectangular box 0 s x < 1,1 s y s 2,1 s z s2.

Q: 7) z dV, E is the solid enclosed by the cylinder r2 +y = 1, and the E planes z = 0 and z 3.

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Q: Evaluate O xy?dx + a°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3)

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Q: Evaluate ∭E sqrt(x2+y2) dV where E is the region that lies inside the cylinder x2+y2=4 and between…

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Q: Evaluate p (x² – 2xy)dx + (x²y +3)dy around the boundary of the region defined by y? = 8x and x = 2…

A: To evaluate : ∮x2-2xy dx+x2y+3 dy around the boundary of the region defined by y2=8x and x=2 (a)…

Q: Use Green's Theorem to evaluate the line integral. cx2 - y?) dx + 5y? dy C: x² + y² = 9 (x² .

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Q: Evaluate J G Y dV where G is the cylinder x² + y² = 4y bounded above by z = 4 and below by z = x² +…

A: The given problem is to evaluate the given triple integral over the given solid region bounded by…

Q: To reduce the DE with linear coefficients (x+2y – 3) dx – (2x+3y – 4) dy=0 to a homogeneous DE, use…

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Q: Integrate h (x. y) xy'i+2j over the indicated path: Brr(u) = (1- u)i. HE [0. 2).

A: Consider the given function and path.

Q: d. .2 The solid bounded by the cylinder x+y = 9 and the planes z = 0 and z = 3- x. %3D

A: The solution of the problem is given in the next steps.

Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (d) z = sin (4x + 5y); x = s + t, y = s - t

A: Given that, z=sin4x+5y ; x=s+t ; y=s-t Then we get, z=sin4s+t+5s-t⇒z=sin4s+4t+5s-5t⇒z=sin9s-t

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: . Solve the following problem with insulated boundaries: Uz = Uxx Ju,(0, t) = 0 lu(1, t) = 0 u(x, 0)…

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Q: Given: Sox?er*+3, dx. Using integration by parts Sucv = uv - Svau), and letting u= f(x), dv= 3 g(x)…

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Q: Evaluate I/| V x2 + y² dV, where E is the region that lies inside the cylinder x2 + y? = 16 and…

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Q: Find the bounded solution of âyở y x> 0, t>0 where y (0, t) = 1, y (x, 0) = 0.

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Q: Evaluate II Væ² + y? dV, where E is the region that lies inside the cylinder æ2 + y² = 16 and…

A: E is the region that lies inside the cylinder x2+y2=16 and between the planes z=-5 and z=4 Change…

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: Find the solution u(x, y) of u+sin(r) uy = y for z, y ER, u(x = 0, y) = 0.

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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: find the indicated extrema, assuming that x, y, and z ar = xyz z - 12 = 0

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Q: Find Vf at the given point. f(x,y,z) = x3 + y2 – 3z2 +z In x, (1,2,4) Vil(1,2,4) =Di+j + ()k ( %3D

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Q: Evaluate dV, where E is the solid in the first octant bounded by r2 +y? + z2 = 1 E and a2 + y? + z2…

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Q: please explain it step by step

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Q: The function f (x,y) =e/*+3tan( y/x) is homogeneous of degree A) 3 B) 2 C) 1 D

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Q: Find the domain. y-Vx Lütfen birini seçin: a. Df = {(x,y): x < 0 ve y < vx} b Df = {(x,y): x < 0 ve…

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Q: If f(x, y, z) = ln(æª + y!0 + z®) + V(x10 + y8 + zª), then find fr, fy and f; at (1, 1, 1).

A: Given, f(x,y,z)=ln(x4+y10+z8)+(x10+y8+z4)

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: To reduce the DE with linear coefficients (X+ 2y - 4) dx – (2x+y-5)dy=0 to a homogeneous DE, use the…

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Q: 1 Evaluate dV, where E lies between the spheres x2 + y2 + z2 = 9 and x2 + y? + z2 x2 + y? + z2 36 in…

A: we want to find the triple integral ∫∫∫E1x2+y2+z2  dVwhere E lies between the sphere x2+y2+z2=9  and…

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: (h) Vx E R, 3y E R, (x + y > 0 or x + y = 0). (i) Vx E R, 3y E R, (x + y > 0 and x + y = 0). (j) (Væ…

A: .

Q: 9. xy sin yz dV, where G is the rectangular box defined by the inequalities 0 <x< T, 0 < y< 1,0 < z…

A: Given information: The integral is ∬∫xysinyzdV and the region is bounded by the rectangular box…

Q: Evaluate I/ V x2 + y2 dv, where E is the region that lies inside the cylinder x? + y2 = 9 and…

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Q: i x Jl plaly da :J,I Ji ull rcos(@), y=rsin(@) التكامل e-(5x2+2y) dxdy

A: We have to use integration using changing the rectangular axis.

Q: Given that f(z) = y – x – 3x²i. Find S f(z)dz OB B-1+i A=i

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Q: To reduce the DE with linear coefficients (x+ 2y – 3) dx – (2x+3y – 4) dy=0 to a homogeneous DE, use…

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Q: 2. Let i = y?x + xŷ + z²ż, and let S be the paraboloid z = x2 + y? with 0 < z < 1. Show that fci. de…

A: Given  v→=y2x^+xy^+z2z^ and S be the paraboloid defined by  z=x2+y2      , 0≤z≤1 The boundary C of…

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: Integrate f(x, y)= y cos xy over the rectangular 0 sxsm, 0 s ys 1*

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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: f(z) dz where a inside r= z-a

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Q: h(r, y) = h(0,0) = 0 3x2 + y2 (i) Prove that |h(r, y)| <ly

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

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Q: If f(x, y, z) = x² y + y² z + z2 x for all (x, y, z) e R3 ar i+ j+ k, then the value %3D and V dy of…

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Q: Evaluate III Vx2 + y² dV E where E is the region that lies inside the cylinder x2 + y2 = 4 and…

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Q: The function f (x,y) =e" + 3tan an( y/x) is homogeneous of degree А) 3 в) 2 cC) 1 D) 0

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Q: (x - y) dv, where E is enclosed by the surfaces z = x² - 1, z = 1 - x², y = 0, and y = 4

A: Consider the given function fx,y,z=x-y.  The region E is enclosed by the surfaces…

Q: Evaluate ||/ Væ² +y? dV, where E is the region that lies inside the cylinder æ² + y² = 16 and…

A: Given :  The integral ∫ ∫ ∫E x2+y2 dV , where E is the region that lies inside the cylinder  x2+y2 =…

Q: An integrating factor (of the form u(x, y) = x" + y") for the DE. ydx + 5xdy = 0 is O is + y * + y?…

A: Solution: The objective is to find the integrating factor of the given differential equation