Q2// If F = 3i + 2j- 2yk , Evaluate F dv where V is region bounded by the plane y=0,z=0,z=x and the surface x2 +y2 = 16

Q: Q1: Evaluate: 2x dV where E is the region under the plane 2x + 3y + z = 6 that lies in the first…

A:

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

A:

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: Q3// A surface S is defined by 2x2 + z = 1 and the bounded by the planes y = 0,y 2, x 0,z = 0 in the…

A:

Q: Consider the double integral //(y - x) dæ dy I = R where the finite region R is bounded by the lines…

A:

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: Evaluate (2r+y) dV _ where V is closed region bounded by the z= 4>x and the planes x = 0, y = 0 and…

A:

Q: Use Green's Theorem to evaluate the line integral. |v² dx + xy dy C: boundary of the region lying…

A: Introduction: The line integral ∫CF·dr geometrically represents the circulation of the function F…

Q: Evaluate F dV where F = 3i+z j+2yk and V V is region bounded by planes z = 0, z = 3 2 and surface x²…

A: here we can use that the volume integral over vector form is simply integral in different direction.

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

A:

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

A:

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

A:

Q: 13. Calculate the flux of F across S.F = (3x, xz, z2) and S is the surface bounded by the paraboloid…

A: Given vector field is  F=3x,xz,z2 we have to find the flux through F where S is the surface bounded…

Q: 11. xyz dV, where G is the solid in the first octant that is bounded by the parabolic cylinder z = 2…

A: To evaluate the triple integral

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

A:

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

A:

Q: Q11// If F = 3xi + 2j – k , Evaluate , F dv where V is region %3D bounded by the plane y=D0,z30,…

A:

Q: Evaluate double integral f.ns where F=xi-yj+(z2-1)k and s is closed surface bounded by the planes…

A:

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

A: Solving this by green theoram

Q: Q3// A surface S is defined by 2x2 + z 1 and the bounded by the planes y = 0,y 2, x = 0,z = 0 in the…

A: A surface S is defined by 2x2+z=1 which is bounded by the planes y=0, y=2, x=0, z=0 in the first…

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

A:

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: Q2// If F = 3i + 2j - 2yk, Evaluate F dv where V is region bounded by the plane y=0,z=0,z=x and the…

A: Given that F=3i+2j-2yk Then , ∫VF dv =∫∫∫V∇.F dv Thus to find ∇.F ∇.F=∂3∂x+∂2∂y+∂-2y∂z Thus, ∇.F=0

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

A:

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

A: Given problem:-

Q: Find the areas of the regions 1. Bounded by the spiral r = 0 for 0 < 0 < T r = 0 2'2 х (п, т)

A:

Q: Evaluate F dV where F = 3i+z j+2yk and V V is region bounded by planes z = 0, z = 3 = 4. and surface…

A: here I am simply using the property that triple integral gives volume and double integration area of…

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

A:

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: Q5// If F = 3i + 2j – 2xk , Evaluate , F dv where V is region bounded by the plane y=0,z=0, z=4-y (z…

A: Given an vector function F. Find the limits of the variables x , y and z. Evaluate the volume using…

Q: Q5// If F = 3i + 2j – 2xk , Evaluate , F dv where V is region bounded by the plane y=0,z=0, z=4-y (z…

A:

Q: 2. Evaluate X+y dz dy dx s is the solid bounded by where the Sur faces with use the Cartesian method

A:

Q: a) Evaluate ||| x²yz dV, where G is solid in the first octant that is bounded by parabolic cylinder…

A:

Q: Use Green's Theorem to evaluate the line integral $. (x2-y2)dx + (2y -x)dy where C consists of the…

A: We will plot the region bounded by two given curves and find the integral using Greens theorem

Q: 3. Use the change of variables: u = x + y , v = y – 2x to evaluate the integral: Cx+y(y-2x)²dydx .…

A: Given: The change of variables: u=x+y and v=y-2x We have to evaluate the integral: ∫01∫01-xx+y y-2x2…

Q: Evaluate the triple integral. 8x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the…

A: The objective is to evaluate the triple integral ∫∫∫E8xdV, where E is bounded by the paraboloid…

Q: 3. Let R be the region bounded by the lines r+ y = 0, x – y = 0, and y = 2. Evaluate the double…

A:

Q: Use Stockes' theorem to calculate the line integral fe F.dr where F (2.52) = (szy + e)i + (2 – Iny)3…

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

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

A:

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: Q5// If F = 3i + 2j – 2xk , Evaluate , F dv where V is region bounded by the plane y=0,z=0, z=4-y (z…

A: Given, F→=3i^+2j^-2xk^Bounded by the plane, y=0,z=0, z=4-yGiven suraface is, x2+y2=16…

Q: Evaluate the triple integral. 10x dv, where E is bounded by the paraboloid x = 2y² + 2z2 and 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: Evaluate 2r+y) dV _where V is closed region bounded by the cylinder z=4x and the planes x = 0, y = 0…

A:

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

A:

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

A: