Evaluate JJ, xy dA, where D is the region bounded by the curves xy = 2,4y = x² and y = 4. а.

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: Use the change of variables X = u, y = uv to evaluate ex dA, where R is the region R in the xy-plane…

A: Solution: The objective is to find the value of ∬ReyxdA where R is the region in the xy-plane…

Q: The area of the region bounded by the curves 2y2 +2 and z 2y+2 is 2. 3 5 -1 -2 16 17 (A) 3 (B) 3 13…

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Q: Evaluate the integral e5xy dA, 2 where R is the region enclosed by the lines y = 3x, y = x, y =, y…

A: Given Region R is Enclosed by : y=3x,y=x,y=1x, y=2x  ⇒yx=3, yx=1, xy=1, xy=2 Let yx=2 , xy=2 1≤u≤3,…

Q: Evaluate ffysin(xy)dxdy น over the region bounded by xy = 1, xy = 4, y = 1, and y = 4 using x == , y…

A: We have to find the area using double integration.

Q: 8. Evaluate y° dx – x° dy, where C is the boundary of the region R = {(x,y) E R² : x² + y² 0}…

A: Applying conditions

Q: Calculate the double integral √ √(8x + 2y + 16) dA where R is the region: 0 ≤ x ≤ 1,0 ≤ y ≤ 4.

A: The objective is to evaluate the double integral.

Q: Evaluate y'dx+ xydy where C is the boundary of the region bounded by y = Vx.y 0, and x 9.

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Q: Evaluate dA where R is the region given by 0sxs 1, 0s y s 1.

A: The question is taken from the calculus in which we have to find the double integral value  so We…

Q: Evaluate (2r+y) dV _ where V is closed region bounded by the z= 4>x and the planes x = 0, y = 0 and…

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Q: Use Green's Theorem to evaluate the line integral. |v² dx + xy dy C: boundary of the region lying…

A: Introduction: The line integral ∫CF·dr geometrically represents the circulation of the function F…

Q: Evaluate the double integral / (3x + 2) dA I D when D is the bounded region enclosed by y = x and y…

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

A: Given: ∫Cy2 dx+xy dy, where C: boundary of the region lying between the graphs of y=0, y=x, and x=25…

Q: Evaluate the double integral |xcosy dA: where R is the triangular region R bounded by the lines y =…

A: To evaluate the integral, first identify the limits of x and y from the region of integration and…

Q: Evaluate fSr f (x, y) dx dy, where R is the region given by 0< x< 2; 0 < y 5 5 and f(x, y) = 1 – –…

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Q: c) Calculate (x+y + 2) dV, where E is the region bounded by r2 + y +z s 25 and above the E xy-plane.

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Q: Evaluate the moment M, and M,y of the region bounded by y = 2x+ 1, x + y = 7 and x = 8.

A: fx = y = 2x+1gx= y = 7-x      Mx=12∫LLULfx2-gx2dx               Moment about x-axisMy=∫LLULxfx-gxdx…

Q: Evaluate the moment M, and My of the region bounded by x = 2y – y² and the y=axis.

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

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

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Q: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the cone z = Vr2 + y²…

A: In cylindrical coordinates,                                                               and…

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

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

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Q: (b) |(x+y)dA} where R is the region bounded by y=Jx and y = x² .

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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: 3. Use the substititutions u = y – x, and v = y +2x to evaluate the integral (2x +y)(x – y) dx dy…

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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: 3. Use a suitable change of coordinates to calculate the integral / x² – y² dA, where R is the R…

A: The region R is given by

Q: Sketch the region R and evaluate the iterated integral ffa (12x+4y) dy dx Ја Јахо f(x, y) dA.

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

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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: Evaluate f S Sp(2+ e(=²+v²+z*)*/²) dV, where B = {(x, y, z) | x² + y² + z² < 9} Describe the region…

A: Consider the provided question, (2) (a)

Q: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the %3D Vr2 + y? with…

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Q: Evaluate the moment Mx and M, of the region bounded by y = 2x + 1, x + y = 7 and x = 8.

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

A: We have to evaluate the integral.

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

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Q: Evaluate the moment M, and M, of the region bounded by x = 2y - y2 and the y=axis.

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Q: Evaluate the line integral Ja? + xy)dx + (x - y²)dy where C is the positively oriented boundary of…

A: we need to calculate the given line integral about C where C is the boundary of the region bounded…

Q: Evaluate || Vx2 +y? dx dy over the region R in the xy plane bounded by x² +y² = 36 - R

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Q: ) Evaluate Sxy dx dy R is the region bounded by x =0, x =2, y = x

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Q: Evaluate the moment My and My of the region bounded by y = 2x + 1, x + y = 7 and x = 8.

A: evaluate the moment Mx and My of the region bounded by y=2x+1 , x+y=7 , x=8

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: SR(xy)dA where R is the region bounded by x=0, y=2x+1 and y=-2x+9.

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

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

A: First I have changed the line integral into double integral with the help of Green's theorem and…

Q: Evaluate (x+ y)dx+ xy dy. where Cis the positively-oriented boundary of the region bounded by the…

A: We have to evaluate the integral                                                  ∮Cx+ydx+xydy Where…

Q: SS ez+ydydx where R is the region bounded by: r = 0, y = 0, x + y = 1. Calculate the value of

A: The given integral is ∫∫Rex-yx+ydxdy where R is the region given as x=0; y=0; x+y=1. Change the…

Q: Evaluate the line integral [2y'dx+(x* +6y°x)dy where C is the boundary of the R region shown below…

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