3. Use the substititutions u = y – x, and v = y +2x to evaluate the integral (2x +y)(x – y) dx dy where R is the region in the first quadrant bounded R by the lines y + 2x = 4, y+2x =7, y – x = 2, and y – x = 1.

Q: Verify Green's Theorem by evaluating both integrals dk + x° dy = /. / dA ду for the given path. C:…

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Q: (b) / = xyz dV if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

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Q: 4. Evaluate S, cos dA where D is the region bounded by D = {(x, y)/ VL < x < v3Ln , 0 < y< x² }.

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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: Evaluate the triple integral. 2xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

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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: ON Verify Green's Theorem by evaluating both integrals 7y dx + 7x*dy = J J]a дм ƏA for the path ду…

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Q: Evaluate E=∭D(x2+y2+z2)−3/2dV where D is the region bounded by the surfaces x2+y2+z2=9 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. |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: 16. Use the indicated change of variables to evaluate the double integral y sin xy dA where R is the…

A: We have to evaluate    ∬Ry.sin xy dA Region Bounded by xy=1, xy=4, y=1 and y=4. We have to assume…

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

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Q: Evaluate the triple integral (x + 2y) dV where E is bounded by the parabolic cylinder y = 7x² and…

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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: 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 integral In(x2 + 1)dx – xdy, C is the boundary of the region…

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Q: Evaluate the integral of the two-form w = (x8 + 2y) dx A dy over the region D bounded by the curves…

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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: Evaluate the triple integral. (x - y) dv, where E is enclosed by the surfaces z = x² - 1, z = 1 -…

A:

Q: Evaluate the triple integral. (x - y) dv, where E is enclosed by the surfaces z = x² - 1, z = 1 -…

A: First, draw the region E, bounded by z=x2−1,  z=1−x2,  y=0, and y=8. The region is bounded below by…

Q: Use Green's Theorem to evaluate the integral [(y-x) dx + (2x−y)dy where C is the boundary of the…

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Q: Evaluate the double integral I = | | (2 – cos(x + y)) dA D when D is the bounded region enclosed by…

A: Given- I=∬D2-cosx+ydA, where D is the region bounded by the lines x+y=π,x=0 and y=0 To find- The…

Q: Evaluate the triple integral ∭E(x+2y)dV where E is bounded by the parabolic cylinder y=2x2 and the…

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Q: Verify Green's Theorem by evaluating both integrals aN y2 dx + x2 dy dA ду - əx for the given path.…

A: For c-1 sign is negative because of opposite direction

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: 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: Use Green's Theorem to evaluate |F.n ds, where F (Va + 4y, 2x + 4y) 2x x2 and the x-axis (oriented…

A: Given F→=x+4y,2x+4y We have to find the ∫CF→⋅n→ds, where C is the boundary of the region enclosed by…

Q: - The region bounded by 2y = x and (x − 2)² = −4y + 12 is revolved about the line y = 4. Determine…

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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: 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: Evaluate the triple integral ∭E (x+7y)dV where E is bounded by the parabolic cylinder y=2x^2 and the…

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Q: 3. Evaluate the triple integral where E is the region behind y = 10 – 2z and in front of the region…

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Q: Evaluate the triple integral. SSS 5x²e" dv I where E is bounded by the parabolic cylinder z = 1 - y²…

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Q: 1 Evaluate the double integral| dx dy where T is the quadrilateral bounded by the lines x = 1, x =…

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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: Use Green's theorem to evaluate the integral for S[(6y-e*) dx +(8x+ lIn(4y)) dy]. where C is the…

A: Evaluate the integral              ∫C6y-e3xdx+8x+ln(4y)dy using Green's theorem, where C is the…

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: b.) xyz dv if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

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Q: Let D be the planar region bounded by y = 0, y = x², and x = 1. The integral ff cos(z² + y²) dA…

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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: 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: Evaluate the triple integral -p (x + 6y) dV where E is bounded by the parabolic cylinder y = 8x² and…

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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: Q1 Verify that [(v ²– 2x )dx +(2xy +x³\dy = | dA where C is the boundary of a region %3D дх ду R…

A: By  apply green theorem

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 the integral ₁²+ y (x+y)e³-²dA, where R is the region bounded by the lines z+y = 1 and 2 +…

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Q: Evaluate the triple integral (x + 8y) dV where E is bounded by the parabolic cylinder y = 4x² and…

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