a) Evaluate ff, (3 – 4x)dV where E is the region below z = 4 – xy and above the region in xy – plane defined by 0 < x< 2, 0 < y< 1.

Q: SI (1 0x°y - 6)ixdy where S is the region bounded by -2y? and Evaluate X = x = y'.

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Q: (d) |// Vx² + y² dV, where P is the region under the cone z = 2 – ry-plane. /x² + y² and above the…

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

Q: 1) Find the volume of the prism whose base is the triangle in the xy-plane bounded by the x-axis and…

A: To find the volume of the prism described we just need to evaluate the given double integral…

Q: Use Green's Theorem to evaluate the line integral. (x – 2y) dx + (x + y) dy C: boundary of the…

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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: ex: Evaluate SS (&++y²)dV over the first octont region boundeol by the cylinders x*ty=/ and xay=4…

A: Convert coordinate system into cylinder coordinate system. Sketch region D and find range of…

Q: Evaluate Slo I –dA, y3(x3+1) where D is the region bounded by x = -y³, х%3D 3 аnd the x — аxis. |

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Q: Determine a region of the xy-plane for which the DE (1+ y) y' = x²will have a unique solution whose…

A: Theorem of existence of uniqueness: If f(x,y) and dfdy are continuous on rectangular region R, then…

Q: Let R be the region bounded by the line y = 4 and the parabola y = x2. Integrate f (x, y) xy – y²…

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Q: H. w: find find the region bounded by x=y-y² Y = 1, revolved about Ⓒx-axi

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

Q: (c) By using the Green's theorem, evaluate $(2xy) dx + (4x²y*) dy if C is the boundary of a region…

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Q: 9. Evaluate 18x dV where E' is the region behind the surface y = 4 - 2² that is in front of the…

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Q: Q1 Verify that [Oy²-2x )dx +(2xy +x² xdy = [[ ƏP dA where C is the boundary of a region R R defined…

A: We have to verify ∫Cy2−2xdx+2xy+x2dy=∬R∂Q∂x−∂P∂ydA, where C is the boundary of a region R defined by…

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A:

Q: Q3// 1. Sketch the region D and Evaluate: [ f(x+y) dA Where D, is the triangle region region in the…

A: Let's solve given double integration.

Q: 4. If C is the boundary of a region bounded by x2 + y? = 16 in counterclockwise manner, use Green's…

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Q: Use Green's Theorem to evaluate f x2 dx+ (xy+y²) dy where C is the boundary of the region R bounded…

A: follow next step

Q: 1. Evaluate , 3y e ²x dA where D is the region bounded by x = ₁x = 1, y = 1 and y = 2. 2

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Q: Q3 Verify Green's theorem in plane for (x² - 2xy) dx + (x²y + 3)dy where c is the boundary of the…

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Q: 1. Find the surface area of the region S in the plane z = 3x + 2y such that 0 <x < 10 and 0 < y <…

A: We have to find the surface area of the region S in the plane z = 3x + 2y such that 0&lt;=x&lt;=10…

Q: 1. Evaluate the double integral r²y dA, where D is the region enclosed by the x-axis and the…

A: We can evaluate the double integral.

Q: Use Green's Theorem to evaluate the line integral. y2 dx + ху dy C: boundary of the region lying…

A: Use green s theorem

Q: 149. sin x cos ydx + (xy + cos x sin y)dy, where C is the boundary of the region lying between the…

A: We have to find ∫c sin x cos y dx +(xy+cos x siny)dy , where C is the boundary of the region lying…

Q: Use Green's Theorem to evaluate the line integral. y2 dx + xy dy C: boundary of the region lying…

A: Given problem:-

Q: / y cos(r*)dA. R

A: Given:- Let R be the region in R2 bounded by the x-axis, the parabola y = x2 and the line x = 2

Q: Evaluate . (y² z)dV where E be the region in the first octant E bounded by the planes x = z, x + z =…

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Q: 11. Let D be the triangular region bounded by the lines y = 1, y = 2x and y = -x. Evaluate the…

A: Given D be triangular region bounded by y=1,y=2x,y=-x.

Q: 2. For the region D enclosed by y = - x, y = 1 – x, y = x, y = x + 2, use an appropriate…

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Q: Evaluate the triple integral. SSSE 7xy dV¸ where E lies under the plane = 1+x+ y and above the…

A: We have to Evaluate the triple integral.

Q: Let A be the region bounded by y = 8x 3(1−x) and the x-axis between x= 0 and x= 1. Find the solid…

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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: Find the maximum and minimum of w(x, z) = 2xz + z^2 +1 in a region R bounded by x = 0, z = 0, and x…

A: The bounded region R is:

Q: 18 Evaluate EUE z(x2 +y? +z?) dV where E is the region described by 2 0szs v1-x -y

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Q: Use Green's Theorem to calculate S,x²y³dx + (xy – y²)dy where C is the boundary of the region lying…

A: Greens Theorem:

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: Line integration by using Greens theorem

Q: (c) Find II zdV where E is the region bounded by the cylinder y² + z² = 9 and the planes E x = 0, y…

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Q: Use Green's theorem to evaluate the integral: 6(-x²y)dx + xy°dy where C is the boundary of the…

A: Let C be a positively oriented, piecewise smooth, simple, closed curve and let D be the region…

Q: x² and t %3D 2) = z where E is the region bounded by the parabolic cylinder y

A: We have to set up the integral according to the given information

Q: 21 Verify that (y² – 2x )dx +(2xy +x²)dy = || dA where C is the boundary of a region ôy -. R R…

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Q: Verify that | (y -2x)dx + (2.xy + x² = [] dA where C is the boundary of a region R ây C R defined by…

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Q: (a) Evaluat e ce + arctan V)dx where C is the region bounded by y=-x,y=-1 and X = 2 %3D %3D %3D

A: Since the questions are not related so there are 6 different questions. We’ll answer the first…

Q: Sketch the region R and evaluate the iterated integral ff- (1-4x+6y) dy dx y -1.0 O -0.5 3 -1 xn-[…

A: The given integral is  ∫01∫02(1-4x+6y) dy dx re write the integral: ∫01∫02(1-4x+6y) dy dx =∫01…

Q: 5) Let D be the region bounded by the curve xy 1 and the line y = = -x. Evaluate the integral xy dA…

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Q: 2. Evaluate Vye"V dA where D is the region bounded by y = x² and y = 4.

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Q: Verify that [y- 2x )dx +(2xy +x²)dy = dA where C is the boundary of a region %3D R R defined by y=0,…

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Q: 3. Use Greens theorem to evaluate (e* + y²)dx + (e' + x²) dy where c is the boundary of the region…

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

A: we have to evaluate the following by using greens theorem

Q: Evaluate // (1+x² + y2) dV, where E is the region bounded E by the surfaces z = 6y2 - 9x², and z = 6…

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