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

Q: Sketch the region R and evaluate the iterated integral f(x, y) dA. (1 – 4x + 8y) dy dx y y y 2.0-…

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

A: From Green's theorem, ∫CMdx+Ndy=∬∂N∂x-∂M∂ydydx If M=y2 ;N=xy, then ∂N∂x=y ; ∂M∂y=2y

Q: Find the value of the line integral  ∮ C (2*y + e^x) dx + (ln(y) + 8*x) dy, where C is a closed path…

A: Let F=Px,yi+Qx,yj be the vector field and C be the boundary of the region D. The Green's theorem…

Q: Evaluate ∭E sqrt(x2+y2) dV where E is the region that lies inside the cylinder x2+y2=4 and between…

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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: Find the area of region enclosed by x = t - t", y =t – t, 0<t < 1 using Green's Theorem.

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Q: Find the area of region enclosed by x t - t*, y = t – t', 0 <t <1 using Green's Theorem.

A: solution is given below

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: Use Green's Theorem to evaluate: So F.ñ ds C where F = (Vx + 6y, 2x + 6y) and C is the boundary of…

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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: Sketch the region R and evaluate the iterated integral f(x, у) dA. x²y? dx dy y y 4 10 8 6 4 6 8 10…

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Q: Let R be the region bounded by the line y = 4 and the parabola y = x2. Integrate f (x, y) xy – y²…

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Q: Find the area of region enclosed by x = t – t“, y =t – t°, 0 <t < 1 using Green's Theorem.

A: The solution are next step..

Q: Verify Green's theorem in the plane for f (32 - Sy*)dz + (4y – 6zy)dy, where C is the boundary of…

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Q: Evaluate the triple integral I = y dV where D is the region in the first octant (x > 0, y > 0, z >…

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Q: Evaluate the double integral // f(x, y)dA over the region D. f(x, y) = 3, D = {(x, y)|0 < x < 1, ² <…

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Q: Evaluate the integral ∭U(x4+2x2y2+y4)dxdydz, where the region U is bounded by the surface x2+y2≤1…

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Q: Evaluate the integral of the two-form w = (a* + 4y) dx A dy over the region D bounded by the curves…

A: Solution:-

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: 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? dx + xy dy C: boundary of the region lying…

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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: 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: 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: 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: Let R be a region bounded by the four planes a = 0. y = 0, z= 0 and æ + y+z=2. Evaluate SSS 24x dV…

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Q: Evaluate the double integral f(x,y)dA if z= f(x, y) = xye*y over the region R, R: 0< y<1 and 0 < x <…

A: When we calculate double integral, if a function is inside the integral, then resultant value will…

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: Let D = {(x, y) | 2 <r S 3, , -<0<0}. Sketch the region D, and evaluate the double integral lp -4y…

A: We will use polar coordinates.

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

A: Greens theorem if u(x,y) and v(x,y) are continuous functions of x and y ;∮  u dx + v dy = ∬(∂v∂x -…

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: Find the area of region enclosed by x = t – t", y =t – t°, 0 < t < 1 using Green's Theorem.

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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: 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 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: 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: 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: Set up and evaluate the integral JJS, ze-(x+y<+z-) dV where Q is the region above the xy-plane…

A: ∫∫∫Qze-(x2+y2+z2)dvQ=x,y,z| hemisphere of radius 5 above XY planeXY- plane ⇒z=0Convert to spherical…

Q: Let D = {(z, ) | 2<r < 3, -Ses 0). Sketch the region D, and evaluate the double integral n -4y dA.

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Q: Evaluate z dV where E is the region bounded between the spheres x² + y² + z² = 1 and x² + y? + z° 4…

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Q: Compute s F=

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Q: Evaluate the double integral f(x,y)dA if z= f(x, y) = xye*y* _over the region R, R: 0 < y < 1 and 0…

A: Given, z=fx,y=xyexy2 And the given range is, 0≤y≤10≤x≤2

Q: ) Use Green's Theorem to evaluate [(x' -x'y)dx+ xy°dy] where C is the boundary of the region bounded…

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

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Q: A. Evaluate and sketch the line integral :1 = f yx dx + (2X – Y)dy around the region bounded by…

A: Greens theorem

Q: Verify Green's theorem in a plane | (xy +x²)dx + x² dy, where C is the boundary of the region formed…

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