Let R be the region bounded by y = 5 sin(x , y = 5(x – 2)²,

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

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Q: Use Green’s Theorem to evaluate the line integral  (x^2 − 2xy) dx + (x^2 y + 3) dy where C is the…

A: The given problem is to evaluate the given integral in the contour using the green's theorem in the…

Q: Find the area of the plane region, 0≤x≤ π²-4 S.U. 4 1.111 s.u. 1 s.u. 2 S.U. bounded by y=sin X. X =…

A: This question can be solved using the concept of area under curves.

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. | (x - 4y) dx + (x + y) dy C: boundary of the…

A: The given integral is ∫Cx-4y dx+ x+y dy,  where C is the region bounded by x2+y2=1 and  x2+y2=16 To…

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

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Q: Use Green's Theorem to evaluate the line integral: 2xy dx + 4x² y² dy Where C is the simply…

A: Use formula of Green's theorem to solve this problem.

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

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Q: Let C be the boundary of the region x² + y? < 1 and (x + y)² < 1 which is oriented counter-clockwise…

A: Here we will find out the required value.

Q: Let C be the boundary of the region x² + y² < 1 and (x + y)² < 1 which is oriented counter-clockwise…

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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: 3. Use Green's Theorem to evaluate (e3x +y²)dx + (sin y – x²)dy where C is the boundary of the…

A: Green's theorem

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

A: We use the change of variable to prive the given equality

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: π Find the area of the plane region, 0≤x≤ bounded by y=sin X. X = and the = 플 1 2 1.111 s.u. O π²-4…

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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: Find the integral ∭U(x2+y2)dxdydz, where the region U is bounded by the surfaces x2+y2=3z, z=3.

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

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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: 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: We have to evaluate the integral.

Q: (b) ( y cos(ry) dA over the region R = {(x, y)|0<x < 1 and 1 < y <7/3}

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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: dA, where R is the trapezoidal region Cos 5. Use appropriate change of variables to evaluate x + y,…

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

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Q: Use Green's Theorem to evaluate |(e* +y²) dr + (+r²) dy where C is the boundary of the region…

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Q: Let f(x,y)=|x|+sin (2x−3y). If R is the region bounded by the quadrilateral of vertices (0,3),…

A: We have to find the given integral according to the given region

Q: Sketch the region enclosed by the given curves. y = 5 cos(3x), y = 5 sin(6x), х%3D 0, x = T/6 y y 5t…

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Q: Sl, Cos () dxdy sin (1) Prove that: I = JJ. x+y where R the region bounded by x+ y = 1,x = 0,y = 0

A: Here we have to prove that       ∫∫R Cos{(x-y)/(x+y)}dxdy = sin(1)/2  Where R is the region bounded…

Q: Let T be the triangular region bounded by the lines x + y = 1, x = 0, and y = 0. Evaluate the line…

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Q: Evaluate x dV , where E is the E region in the first octant bounded by the sphere x² + y² + z² = 1…

A: given region is in the first octant. using spherical coordinates x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ and…

Q: Use Green's Theorem to evaluate the line integral $. (x2-y2)dx + (2y -x)dy where C consists of the…

A: We will plot the region bounded by two given curves and find the integral using Greens theorem

Q: 4. Evaluate the double integral x cos y dA; R is the triangular region bounded by the lines y = x, y…

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Q: Let f(x,y) = K (x² + y²) IA (x,y) where A is the region bounded by y=1x1 and y=2. Find K so that *…

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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: Use Green's Theorem to evaluate (eš + y³)dx + (sin y – x²)dy where C is the boundary of the region…

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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: Let C be the boundary of the region x + y ≤ 1 and (x+y) ≤ 1 which is oriented counter-clockwise…

A: Given- Let C be the boundary of the region x2 + y2 ≤ 1 and x + y2 ≤ 1 which is oriented…

Q: If 'V' is the region bounded by the planes x = 0, x = 2, y = 0, z = 0 and z+y = 1 then the value of…

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Q: 3. Let R be the region bounded by the lines r+ y = 0, x – y = 0, and y = 2. Evaluate the double…

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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: xyz dV where E is the region bounded by = y², x² = y, z = xy y z = 0.

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Q: Verify Green's theorem in the plane for S(3x² -8y )dx +(4y-6xy)dy, Where C is the boundary of the…

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

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