Q4) Use the Jacobian to evaluate ( sin (x +3y) xdy where 1+(x - y) 2 is the region enclosed by: x +3y = 0, x+3y /2 x -y -0, X-y 1

Q: Q1: Evaluate: 2x dV where E is the region under the plane 2x + 3y + z = 6 that lies in the first…

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Q: 12. In the xy plane the region D is bounded by the lines y = 2x + 6 y = 2r +1, y = -3r +6, and y =…

A: Given: y=2x+6 y=2x+1 y=-3x+6 y=-3x+1

Q: 3(x + y) cos (x2 - y?) da, where R is the rectangle enclosed by the lines x - y = 0, x – y = 6, x +…

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Q: Sketch the region R of integration and switch the order of integration. V 64 - x2 f(x, y) dy dx 5 X…

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Q: a) Evaluate [(2x- y' )dA over triangular region R enclosed between the lines y = -x +1, y = x+1 and…

A: Given integral is ∫∫R2x-y2dA, where R is the triangular region R enclosed between the lines y=-x+1,…

Q: A flux is given by F = x²y³ i – xy j. Verify the Green's theorem for the region bounded by the…

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Q: Integrate f(x, y, z) = x over the region in the first octant (x 2 0, y 2 0, z 2 0) above z = y2 and…

A: Given that,

Q: Po Prove that fcz) = zis coutinuous at z=z. O Prove that. fZキ2。 is dis continnity at z=Zo, where Zn

A: (1) we have to prove that                                                              f(z)=z2 is…

Q: 5. D is the region in the xy-plane bounded by the curves x = cos(y), 3y 27Tx, Зу 3 — 2тх. Evaluate x…

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Q: - The region bounded by y = 2 -x, y = 0, x = 1, x = 2 is rotated about the x axis. 197/12

A: volume generated by revolution of the solid is 19π12 detailed solution with explanation is given…

Q: 9. Use Green's Theorem to evaluate (e* +y²) dx +(e" +x²) dy where C is the boundary of the region…

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Q: W= Pcxiy,Z) = In (x+y+z) ,x= cost, 2. %3D 2X = Cost, y- Sint and z= 4VE >use chain rule to Rind dw…

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Q: 3. Find the circulation of F 2xi + 2zj +2yk around closed contour %3D

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Q: Sketch the region enclosed by the given curves. y = tan(7x), y = 2 sin(7x), -77/21 sxs 7/21 y y 3 3…

A: For sketching the region y=tan7x, y=2sin7x, -π21≤x≤π21. Let y1(x)=tan7x, y2(x)=2sin7x, -π21≤x≤π21 We…

Q: Use Green's Theorem to evaluate the line integral (y – x) dx + (2x – y) dy for the given path. = x²…

A: Green's Theorem: By Green's Theorem we have for a differentiable function f(x,y)=M(x,y)+N(x,y) and a…

Q: 8. Use Green's Theorem to calculate f, x?y³dx + (xy - y?)dy where C is the boundary of the region…

A: The given integral is ∫Cx2y3dx+xy-y2dy, where C is the boundary of the region lying between the…

Q: Sketch the region R of integration and switch the order of integration. F(x, y) dy dx y 2 2 -4 -2 2…

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Q: 2- Find D xyz dV where D is the region with -1 ≤x≤1, x ≤ y ≤ 1, above z = x, and below z = y + 2.

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Q: find the region endlased R by the cunes V=12-2y +1 and Y= -2+2x ャ4.

A: Answer

Q: The solid bounded by y = 4, z = x², z = 2y, and z = 4.

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Q: Eraluate: 1. JJR e-(n^²+yv) the eincles of padii 1& 2 dady, R is the region of between.

A: As per the our guideline, we are supposed to solve only first question. Kindly repost other question…

Q: and the y-axis. 2. Evaluate , 5x³ cos(y³) dA, where D is the region bounded by y = 2, y =:

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Prove that: 1- Cos (2) dxdy (¹) where R the region bounded by x+y=1,x=0.y=0

A: Given integral I=∫∫Rcosx-yx+ydxdy Where R is bounded by x+y=1x=0y=0

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: Integrate f(x, y, z) = x over the region in the first octant bounded above by z = 8 - 2x 2 - y2 and…

A: Given that, z=8-2x2-y2        ...(1)z=y2              ...(2)

Q: 2. Evaluate [(3yz)dV where B is the region in the first octant lying below the plane x + 2y +2: = 4.

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Q: Evaluate the solid bounded by 2x+z=2 and (x-1)2+y2=z.

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Q: The solid bounded by z = x, z = 2 – x², z + y = 3, and y = 0

A: Volume of a solid is obtained using triple integration by the formulae =∫∫∫dx dy dz The solid is…

Q: The centroid of the region bounded by sin x < y< cosx, and 0<x<7/4 is, TV2-4 b) 1 1 a) 4(42 +1) 4(v2…

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Q: 9. The solid bounded by x = 1 – y?, z = y², x = 5, and z = 9.

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Q: 4| ind Volumes of のnen reo リュー! )ス"0) reten iegTon 1- dv - dzdy chy 1 Limik of 2:0> y2 Limik of y:…

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Q: 2. The area bounded by y = -(x - 1)2 + 4, and the lines x =1, y = 2, and y = 4 rotated about the %3D…

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Q: A region R is bounded by the graphs of y=0.5 Vx and y=0.5x. Find the moments Mx and My of R about…

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Q: f(x, y) - x/y over the region in the first quad- rant bounded by the lines y = x, y = 2x, x = 1, x =…

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Q: R is the region bounded by the lines y = x, y = -x, and x = 1. %3D

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Q: 1- Integrate The furction F(X,y= over The region bounded byrj=X7y=2x9 x =1/X=?

A: According to our company guideline if multiple questions are posted we must do only first. You can…

Q: The path integral fv· dr, where v = (sin y, x – cos y) and C is the perimeter of the triangle formed…

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Q: 3, Let R be the of: y: sinx region endlosed bu the grophs n enclosed by and 1 x70 . Groph R and…

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Q: Compute s F=

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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: O R is the region bounded by y = 2 – x² and y = x² – 6. - %3D

A: 5.)  y=2-x2  and  y=x2-6 red line y=2-x2 blue line y=x2-6

Q: 4. Evaluate x²dV G where G is a solid that lies in the first octant bounded by x? + y? = 3z and z =…

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Q: Use the transformations u = xy and v=xy* to evaluate ff xyd4 where R is the √√3 1 X region bounded…

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Q: 8. Evaluate the line integral (x'dx+ xe"dy where C is the closed path along the triangle in the…

A: Here we have to evaluate the integral ∫cx2dx+xe-ydy where C is the closed path along the triangle in…

Q: The region is bounded by y = x³, y = 2x + 4 and y = −1. Then Arearegion = [₁ f(x) dx + f[ g(x) dx,…

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Q: 10. The solid bounded by y = 4, y – x = 1, z = x², and z = = 4.

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Q: 12. Find the outward flux of F = x*yi-cyj+zk across the boundary of the region which is bounded…

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Q: 2. The solid in the first octant bounded by the planes x = 0, y = 0, z = 1, z = 2 – y, and the…

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