4. Consider the following region with three holes, D. Let curl (F) = -4 and F. dī = 7 C2 F. dř = 6 | F. dř = 4. (A) Write the boundary of C = ƏD as a sum or difference of C1, C2, C3, and C4.4 (В) Use Part (A) to write the generalized statement of Green's theorem. (C) Use Part (B) to compute F-dř. C1 C2 C3 C4 Mathnal -6 -3 3 4 6. -1 D

Q: Given that p, = x² +xy, calcultae p, ds, over the region, y <x,0 <x < 1.

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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: (2) Sketch the following region R. R= {(r,0) : 1<r < 3, 1/2 <0< 2n}

A: Sketch the following region R

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.

Q: Evaluate the double integral. / 4x2sin y²dA; R is the region that is bounded by y = x³, y = -x³, and…

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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: 2. Evaluate the double integral / 1OxydA, where D is the triangular region with vertices (0,0),…

A: ∬D10xy dA where D is a triangular region with vertices 0,0,1,2, and 0,3.

Q: Given that C is the boundary of a region bounded by y=-9+x', y =x-3, x 2 and y = 0 with positive…

A:

Q: Evaluate using Green's Theorem ф худх + (х + уjdy Where C is the boundary of the region between x? +…

A: From Green's theorem:   ∮F1dx+F2dy=∬∂F2∂x-∂F1∂ydxdy   Given:   I=∮xydx+x+ydy   F1=xy⇒∂F1∂y=∂…

Q: Use Green's theorem to evaluate O(1-y') dx+(x³ +e" ) dy , where C is the boundary of the region…

A: The integral is ∮C1-y3dx+x3+ey2dy where C is the boundary of the region between the circles x2+y2=4…

Q: If R is a region bounded by y = x² and y = 4x – x², evaluate S. | (x + y)dA R

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Q: Consider the region D in the ry-plane which is bounded by the following 2 4 = x and y = 3r. Compute…

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Q: Use Green's Theorem to evaluate n ds, where F = (Va + 5y, 4x + 5y) and C is the boundary of 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. C:…

A:

Q: Given that C is the boundary of a region bounded by y =-9+x, y = x-3, x= 2 and y = 0 with positive…

A:

Q: 3- calculate SSm xe' dxdy -if the bounded set M is given by inequalities y <2 - x, y 2 x². -Draw the…

A: The region y≤2-x isThe region y≥x2  is The region M is,

Q: Sketch the region D = {(x, y, z): x2 + y2 ≤ 4, 0 ≤ z ≤ 4}.

A:

Q: SI xyz dW, B is region bounded by two cylinders, wwwm w В x^2 + y^2 = 16, x^2 + z^2 = 16, and the…

A: Consider the given volume of the two intersecting cylinders given by  x2+y2=16 andx2+z2=16  as shown…

Q: Sketch the region enclosed by the given curves. x = 9y2, x = 28 + 2y2 y y 21 35 30 1 25 20 5 10 15…

A: x=9y2,  x=28+2y2 The region is,

Q: Use LT  and one other method  to find the PS of x' = y +z+1   y' = z+ x + 1 Z'= x+y+ 1    with…

A:

Q: Use Green's Theorem to evaluate: • dr C where F = (Vx + 3y, 2x + 3y) and C is the boundary of the…

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Q: Given that c is the boundary of a region bounded by y=4-2,y= -x+2, X =1 and y=0 with positive onient…

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Q: Let D be the trapezoidal region in the xy-plane bounded by the graphs of x = 0, y = 1, y = x and =…

A: We will solve the problem.

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: 3. Evaluate JS Vr2 + ydA, where R is the region bounded by the circles with center (0,0) and radius…

A: (3) Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: Given that R is the region bounded by the curve y = x+3 and line y = x-3. (c) By using the limits in…

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Q: If the region R is bounded between two circles x² + y? = 1, x + = 4, then we have: ev+ dr do dA = +…

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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: Use Green's Theorem to evaluate nds, where F = (Va+ 3y, 2a + 3y) C is the boundary of the region…

A: Given Vector field is  F=x+3y, 2x+3y Comparing with F=P,Q, we get  P = x+3y            and…

Q: as Find Hhe voleime of odid generated by revolving tthe region bounded by graphs of y=xe;y 0, and…

A:

Q: Let D be the trapezoidal region in the xy-plane bounded by the graphs of x = 0, y = 1, y = x and y…

A: Here I am attaching image so that you understand each and every step.

Q: (2) Consider the region D in the ry-plane which is bounded by the following 2 4 curves y =, y = ỷ =…

A:

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 (y – x) dx + (2x - y) dy for the given path. C:…

A: Use greens theorem

Q: 1 2 Compute R dA where Ris the region above.

A:

Q: Use Green's Theorem to evaluate nds, where F = (Va+ 6y, 3x + 6y) C is the boundary of the region…

A: Given that        F = &lt; √x + 6y , 3x + 6y &gt; C is the boundary of the region enclosed by y=x-x2…

Q: The value of the double integral // (2x²y + 9y') d A, D where D is the region bounded by x and y = 2…

A: Given problem:-

Q: Use Green's Theorem to evaluate rids, C where F = (Va + 6y, 3x + 6y) C is the boundary of the region…

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Q: Sketch the region R whose area is given by the iterated integral. r 64 - y2 Хр хр 6 4 6 2 4 10 20 30…

A: Given integration is, ∫-88∫064-y2dxdy The region of integration is bounded by, x=0, x=64-y2, y=-8,…

Q: Let D be the region bounded by (a) y = (0 < a< 1),

A: As many parts and its further sub parts are given, so I will solve only one ( Question (a) and its…

Q: Let C be a simple closed curve bounding a region Din R2. which of the following are equal to the…

A: Let C be a simple closed curve bounding the region D in R2.  So using Green's-Theorem,

Q: 17. Let R be the region between the graphs of y = 1 + e* and y = 1-e* on [0, In 2]. Find the center…

A: Here, f(x)= 1+ex g(x)=1-e-x a=0 and b=ln2

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

A:

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: Choose the four correct steps (in order) involved in finding the value of integral M,av where the…

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Q: 2. Evaluate , dV, where o= 45 x²y and V is the closed region bounded by the planes 4x + 2y +:=8, x=…

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Q: O R is the region bounded by x² + y – 4 = 0 and x – y +2 = 0 an is revolved about y = 0.

A: We use washers method to find the integral of that evaluate the volume of the solid of revolution.

Q: 3. Given that p, = x + xy, calculate f,p, dS over the region y sx", 0 < x < 1.

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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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Q: ral by making an appropriate change of variabl re R is the region enclosed by the lines y = 6x

A: