1.Let D=6xy ax+ 2(xz+3z2)ay+3yz az C/m2.Evaluate the surface integrals to find the total charge enclosed in the rectangular parallelepiped 0 < x < 3, 0 < y < 2, 0 < z < 4.

Q: 2. Let D = 2xyā, + 2(x² + z²)d, + 4yzd, C/m² and evaluate surface integrals to find total charge…

A: given D→=2xy ax→+2x2+z2 ay→+4yz az→ it is known that ρ=∇·D→ it is known that…

Q: Calculate :/ F. ds, where F (x, y, z) = (-6x³ + 2yz)i + (-6y³ + sin¯¹ (3xz)) j+ (2z+cos (3x²y²)) k…

A: Given F(x,y,z)=-6x3+2yzi^+-6y3+sin-13xzj^+2z+cos3x2y2k^ and S is the outward-oriented surface of the…

Q: 7. Sketch the surface 15zs9-x' - y² and x'+y' <1

A: To find:

Q: 2. Calculate the centroid of the thin plate R which bounded by a = 1, y = 0 and, x² + y² = 4.

A:

Q: Compute the surface area of the surface generated by revolving the curve c(t) = (t, e') about the…

A:

Q: 8. Use polar coordinates to integrate f(x, y) = x² + y2 over the region in the first quadrant…

A:

Q: Let C be the circle centered at the origin with radius 4 oriented clockwise, and let F(x, y) = (2x +…

A: Given: The vector field across the circle C centered at the origin with radius 4 oriented clockwise…

Q: Evaluate the surface integral , 2zds; o is the part of the following tetrahedron bounded by the…

A: We have to evaluate the surface integral ∬σ2zds where, σ is the part of the given tetrahedron…

Q: Use Stokes' Theorem to compute 1 z? dx + (ry) dy + 2020 dz, where C is the triangle with vertices at…

A: Given I=∮C12x2+xydy+2020dz where C is the triangle with vertices at 1,0,0 , 0,2,0 , 0,0,2 traversed…

Q: Find the equatioa of tangeut plane to the surface + 2y? + 3: = 21 which is puraliel to the plane 2r…

A: parallel to plane 2x+4y+6z = 3      surface x2 + 2y2 + 3z2 = 21     Let  F = x2 +2 y2 + 3z2 = 21  we…

Q: Find the parametrization r(t) = [x(t), y(t), z(t)] of the curve obtained by intersecting the…

A:

Q: 7. Find the length of the curve y (r + 4)/2 on the interval [0,3] 8. Set up, but do not evaluate, an…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 9. Find the surface area of the paraboloid z = x²+y²/2 which is outside the cone z = √x² + y².

A:

Q: F(1, y.:)= (x², 2x²y*, 5yz*) Given: Find (a) div F (b) curl F

A:

Q: 2 A circular wire hoop of constant density 8 = 2 lies along the circle x² + y² = 8a² in the…

A: Given: The density of the circular wire hoop is δ=2, and it lies along the circle x2+y2=8a2 in the…

Q: Suppose F 2.xz + 3y²) ay + (4yz²) az. (a) Calculate fLL F dS, where S is the shaded surface in…

A:

Q: 4. Find the area of the surface obtained by rotating the curve x²/3 + y>/3 = 1, 0 <y<1 about y-axis.

A: If the curve defined by the parametric equations x=x(t), y=y(t)  with a≤t≤b , is rotated about the…

Q: Find the points on the ellipsoid x² + y²/4 + 2²/9 = 1 that is closest to (1, 2, 3).

A: Let (x, y, z) be the points in the ellipsoid closest to (1,2,3) then using the distance formula…

Q: y = e*, 0 <x < In2 around the Ox- axis of the curve segment Calculate the area of the surface formed…

A: We have to calculate the area of the surface formed by the rotation of the curve y=ex, 0≤x≤ln2 about…

Q: 6. Use Green's Theorem to evaluate the line integral fc 2xy dx + (x² + y²) dy, if C is the ellipse…

A: Let R be simply connected region with a piecewise  smooth boundary  'C'. If functions 'M' and 'N'…

Q: ) Find the points on the ellipsoid 6x² + y² + 3z² = 4 where the tangent plane is parallel to the…

A: