A flux is given by F = x²y³ i – xy j. Verify the Green's theorem for the region bounded by the triangle with vertices (0,0), (1,0) and (1,2).

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: Let S be the boundary of the region 0 < z < 25 – x² – y². Use the divergence theorem to evaluate the…

A: Gauss divergence theorem helps to find the required flux if the region is the bounded region. The…

Q: Evaluate the double line integral S  of the fuinction (x − 2y + z) dS. S: z = 9 − x,  0 ≤ x ≤ 9,  0…

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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: Find [[fw ryz dV if W is the solid region in R³ below the surface z = x² + y² and above the square 0…

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Q: A region R is bounded by the graphs of  y=0.8 (x)^1/2 and y=0.8x.  Find the moments Mx and My of R…

A: Given,

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 J, (2x + y) dV, where V is closed region bounded by the cylinder : = 4 – and the planes 4.…

A: Q. Evaluate ∭V(2x+y)dV, where V is closed region bounded by the cylinder z=4-x2 and the planes x=0,…

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…

A:

Q: Determine a region of the xy-plane for which the DE (1+ y) y' = x²will have a unique solution whose…

A: Theorem of existence of uniqueness: If f(x,y) and dfdy are continuous on rectangular region R, then…

Q: Find the average value of the square of the distance from the point P(x, y) in the disk x2 + y2…

A:

Q: Evaluate the moment M, and M,y of the region bounded by y = 2x+ 1, x + y = 7 and x = 8.

A: fx = y = 2x+1gx= y = 7-x      Mx=12∫LLULfx2-gx2dx               Moment about x-axisMy=∫LLULxfx-gxdx…

Q: compute the line integral f(x, y) ds for the given function and path or curve. f(x, y) = x – y, the…

A: Given: fx,y=x-y To Find: Line integral ∫Cfx,yds over the unit semi-circle x2+y2=1, y≥0

Q: Evaluate the moment Mx and My of the region bounded by x + 2y = 6, x = 0 and y = 0.

A:

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

A:

Q: + y^5)dy] where C is the unit circle x^2 + y^2 = 1 traversed counterclockwise.

A: we have to compute the given integral ∮x5+y3dx-(x3+y5)dy     where C is unit circle x2+y2=1.C

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

A:

Q: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the cone z = Vr2 + y²…

A: In cylindrical coordinates,                                                               and…

Q: The value of $ $(2xy - x²) dx + (x+y2) dy, where C is the enclosed curve of the region bounded by…

A:

Q: e dV where E is bounded by the parabolic cylinder z = 1 -y and the planes Evaluate the triple…

A:

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: a) Evaluate ff, (3 – 4x)dV where E is the region below z = 4 – xy and above the region in xy – plane…

A: To evaluate the given triple integral.

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

A:

Q: Evaluate xy dV where E is bounded by the parabolic cylinders y = x², x = y² E and the planes z = 0…

A:

Q: Among all rectangular regions 0&lt;=x &lt;=a, 0&lt;=y&lt;=b, find the one for which the total…

A:

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 |(e* +y²) dr + (+r²) dy where C is the boundary of the region…

A:

Q: Let f(x,y)=|x|+sin (2x−3y). If R is the region bounded by the quadrilateral of vertices (0,3),…

A: We have to find the given integral according to the given region

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

A:

Q: 2) Find the outward flux of F across the region D where F(x, y, z) = (In(x² + y²), –tan'(), zVx² +…

A:

Q: Given that the total flux across the surface, S of the tetrahedron bounded by the planes x= 0, y=0,…

A: Given Vector field is F = 2xi + 3yj - zk

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: 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: 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: Given that the total flux across the surface, S of the tetrahedron bounded by the planes x=0, y=0.…

A: To draw graphs in 3d we need to find intersections with co ordinate axes and also with co ordinate…

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: Find M Myr and (x, y) for the laminas of uniform density p bounded by the graphs of the equations. y…

A: The equation of the lamina are, y=fx=x y=gx=13x

Q: Find Mx, My, and (x, y) for the laminas of uniform density p bounded by the graphs of the equations.…

A: Given:y=x+1,y=x4+1

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

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: Compute s F=

A:

Q: Evaluate the triple integral. 5xy dV, where E lies under the plane z = 1 + x + y and above the…

A: Given that z=1+x+y The range of the variables are, 0≤x≤10≤≤x0≤z≤1+x+y Then, the integral is,…

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

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: Evaluate ſ, z dV where E is bounded by the plane x + y = 2 and the cylinder y? +z² = 1 in the first…

A: Given that, ∫∫∫EzdV, where E is bounded by the plane x+y=2 and the cylinder y2+z2=1 in the first…

Q: Evaluate the triple integral. xyz dV, where G is the solid in the first octant that is bounded by…

A:

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

A:

Q: Set up the triple integral 8y dV, where E is bounded by the coordinate planes and the plane x + y +…

A: To Set up the triple integral for 8y dV, where E is bounded by the coordinate planes and the plane x…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.