Use Green's Theorem to calculate S,x²y³dx + (xy – y²)dy where C is the boundary of the region lying between the graphs of y = x and y = x² orientated in the counterclockwise direction.

Q: (d) |// Vx² + y² dV, where P is the region under the cone z = 2 – ry-plane. /x² + y² and above the…

A: Since you have asked for a multiple question, we will solve the first question for you. If you want…

Q: Evaluate JJ, xy dA, where D is the region bounded by the curves xy = 2,4y = x² and y = 4. а.

A:

Q: .Find the exact value of the double integral. J (2x + 5y) dA, where R is the rectangular region…

A:

Q: A flux is given by F = x²y³ i – xy j. Verify the Green's theorem for the region bounded by the…

A:

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

A:

Q: and y = 2u, evaluate the integral xy³dA where c) Using the transformation x =-; 6u region R is…

A:

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

A:

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

A:

Q: Evaluate ffS. Vx² + y² dV, where E is the region tha lies inside the cylinder x? + y² = 16 and…

A:

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

A:

Q: use the divergence theorem to compute: F(x,y,z)=x2i+y2j+z2k; for the boundary of the solid region…

A:

Q: (c) By using the Green's theorem, evaluate $(2xy) dx + (4x²y*) dy if C is the boundary of a region…

A:

Q: (z+ y – 1) cos D

A:

Q: Sketch the region R and evaluate the iterated integral (x, у) dA. - 2x + 8y) dy dx y y 2.0- 2.0- 1.5…

A: In this question, Firstly, we sketch the region and after that find iterated integral.

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

A:

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: Q3 Verify Green's theorem in plane for (x² - 2xy) dx + (x²y + 3)dy where c is the boundary of the…

A:

Q: find the region endlased R by the cunes V=12-2y +1 and Y= -2+2x ャ4.

A: Answer

Q: 3. Evaluate /// 2* dV if G is a solid in the first octant bounded by the plane y + z = 2 and the…

A: triple integral

Q: Let A be the region bounded by y = 8x 3(1−x) and the x-axis between x= 0 and x= 1. Find the solid…

A:

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: Calculate the Pntegrals over the defined region . y=-2x and y=1-2x on paralleberaM clased with Rhes.…

A:

Q: lad Use Green's theorem to evaluate y² dx + 3xy dy, where c is the boundary of the semi annular…

A: Given Problem:- Use Green's theorem to evaluate ∮cy2dx+3xydy where c is the boundary of the semi…

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

A:

Q: Evaluate zdV where E is the region under the plane 4x + 2y + z = 4 in the first octant ( E х, у, z >…

A:

Q: Sketch the region R and evaluate the iterated integral | Rx, y) dA. 2x + 8y) dy dx y y y y 2.0 2.0-…

A: Given problem:-

Q: Calculate the surface integral ffs F - dS for F(x, y, z) = (xª, –x³z surface bounding the region…

A:

Q: (c) Find II zdV where E is the region bounded by the cylinder y² + z² = 9 and the planes E x = 0, y…

A:

Q: Let D be the solid region bounded above by z = -5x² +y? and below by z =-5. Then the projection of D…

A:

Q: Q7. Use Green's theorem to evaluate y² dx + 3xy dy, where c is the boundary o the semi annular…

A:

Q: Verify that | (y -2x)dx + (2.xy + x² = [] dA where C is the boundary of a region R ây C R defined by…

A:

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

A:

Q: 2. Let R be the region in the first quadrant of the xy-plane bounded by the hyperbolas xy = 1, xy =…

A:

Q: (a) Calculate the centroid (7, y) of the region under the graph y = cos x for 0 < x <T/2.

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

Q: Use the given transformation to evaluate the integral. (3x2 - 3xy + 3y2) da, where Ris the region…

A:

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

A:

Q: 1. Verify Green's theorem in the plane for 6 (3x- 8y) dx + (4y – 6xy)dy, where C is the boundary of…

A:

Q: 16. Use the Divergence Theorem to find the outward flux across the boundary of the region D where F…

A:

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

A:

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,…

A:

Q: Use the transformation (change of variables) x = 2u +v and y = u+ 2v to set up the integral / (x –…

A:

Q: (a) Integrate g(x,y,z) = Inx²+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

A:

Q: where E is the region bounded by the paraboloid y= r+ z2 (Figure 15.4. %3D y = x2 + z?

A: Please rate and feel free to ask any query about any part of the question .

Q: Use the transformation u = x2 - y? and v = 2xy to evaluate (x2 + y2)dx dy for the R region R bounded…

A:

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

A:

Q: Verify Green's theorem in the plane for (3x² -8y²)dx+(4y-6xy)dy, where C is the closed curve of the…

A:

Q: Evaluate the line integral [2y'dx+(x* +6y°x)dy where C is the boundary of the R region shown below…

A:

Q: Find the value of a if the centroid of the region bounded by the parabola y² = 4px and the line = a…

A:

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

A: