Q1 Verify that [Oy²-2x )dx +(2xy +x² xdy = [[ ƏP dA where C is the boundary of a region R R defined by y= 0, x = 1, and y = x. Hint: Here P= y’ - 2x and Q=2xy + x² .

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: 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 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: Suppose D is the region bounded between the z-axis, the curve y = e", and 0 <I<1. Compute the…

A: We need to compute the integral: ∫∫D2ydA Given that, y=ex and 0≤x≤1.   Using some integral formulae…

Q: (b) Verify Green's theorem for |(x² – 2x y)d x+(x² y+3)d y, around the boundary e of the region y…

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Q: The double integral 2xy³dA over the rectangular region R {(x, y) E R“, 0 < xS 4 and – 1 S y< 0} is…

A: The double integral ∬Rfx, ydA can be written as ∬Rfx, ydxdy. We have given the rectangular region as…

Q: Verify Green's Theorem by evaluating both integrals ƏN y² = / / dx + x2 dy dA - Əx ду for the given…

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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: 3. Sketch the region and evaluate the iteraterd integral (a²y – ry?)dydx. 2.0 1.5+ 1.0 0.5 0.0 0.0…

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Q: 2 Evaluate 2 dA where D is the region described by 0s ys 55 - x Integral is equal to : Enter an…

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Q: Verify Green's Theorem by evaluating both integrals aN dx + x² dy = / / dA ay y2 ax for the given…

A: To verify green's theorem by evaluating both the integrals.

Q: (i) Evaluate the double integral (x + y) dxdy where D is the triangular region in the xy plane with…

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Q: Q3)Verify the Greens theorem to the integral f(2x*y-x)dy +(2yx- y)dx where C is atriangle its…

A: Green's theorem

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

A: The given integral is                                    ∫Cy-xdx+(2x-y)dy for the given path.…

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

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Q: Use Green's Theorem to evaluate the integral (v-x) dx + (2x−y)dy for the path C. boundary of the…

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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: Verify Green's Theorem by evaluating both integrals ƏN y2 dx + x² dy dA ay for the given path. C:…

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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: 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: 4. Evaluate fe cosy dx + (xy – xsiny) dy where C is the boundary of the region lying between the…

A: Given  ∫Ccosydx+(xy-xsiny)dy

Q: Verify Green's theorem in plane for (x* - 2xy)dx + (x°y+ 3)dy where c is the boundary of the region…

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Q: Use Green's Theorem to evaluate the line integral. by² dx + xy c C: boundary of the region lying…

A: The objective of the question is evaluate the definite integral using Green's Theorem.

Q: 1. Compute fSSp(z+1)°dV where E is the region lying inside the sphere x² +y² + 22 = 1 of radius 1…

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

A: The objective of the question is evaluate the integral help of Green's Theorem.

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) Evaluate the triple integral. | 6xy dV where E lies under the plane z = 1+x + y and above the…

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

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Q: Evaluate  DOUBLE integral xy dA, where D is the region bounded by the line  y = x − 1 and the…

A: Given: The bounded regions are, Find the points where the bounded regions intersect. Substitute…

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. | 2xy dx + (x + y) dy C: boundary of the region…

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

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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: 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: Calculate the double integral / Rx cos(2x + y) dA where Rl is the region: 0 <x<,0 < y< 6. 2

A: Here we have to find the value of double integral.

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: 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: 2. Find the value of the line integral foF dr without using Green's Theorem, where F(x, y) = (x+y)i…

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Q: The double integral ſſ 2xy³dA over the rectangular region R = {(x, y) E R“, 0< xS 4 and – 1< y< 0}is…

A: Dr

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: 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: 4. Compute the value of the double integral fSRe-xydxdy, where R is the region bounded by the lines…

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Q: Verify Green's Theorem by evaluating both integrals ƏN [< y² dx + x² dy = √₂₁ / (™N - 3W) CIA dA əx…

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

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Q: 8) consider the region R in the first quadrant(xz0, y2) bounded by x=2y² X=Y²+1 a) set up, but clo…

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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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