4. Use Cartesian coordinates to set up the iterated double integral given by Iff v² av D where D is the tetrahedron in the first octant bounded by the plane 2x + 3y + z = 6. Use I 1:1 D

Q: 3. Given f(x, y, z) over the tetrahedron T defined by 2x - 3y - 6z = 6 and the three coordinate…

A: See the graph of T Plane 2x-3y-6z=6 and three coordinate axes

Q: Evaluate the surface integral. JS (x+y+z) dS, S is the parallelogram with parametric equations x = u…

A: We find the surface integral.

Q: Set up the integral (do not evaluate) in (u, v) coordinates to find the integral SSRx + y dA, where…

A: The given integral is ∬Rx+ydA over the region R which is a parallelogram with vertices…

Q: 3. Use spherical coordinates to calculate this integral of f(x, y, z)=√√² + y² + 2² over the region…

A:

Q: Find the area of the surface cut out from the bottom of the paraboloid z = x² + y² by the plane z =…

A:

Q: 24 dA - I 3x – Y when D is the parallelogram bounded by x – 2y = 0, x – 2y = 2, - and Зх — у 3D 1,…

A:

Q: Evaluate the surface integral (2ayi – yzj + zk) · dS. Where S is the part of the paraboloid z = a2 -…

A: We have to evaluate the integral ∬S2xyi^−yzj^+zxk^⋅dS where S is the path of the paraboloid…

Q: The region W lies between the spheres x² + y² + z² = 4 and x² + y² + z² = 16 and within the cone z =…

A:

Q: C is the intersection curve between the paraboloid z=x²+y² and

A: Given that C is the intersection curve between the paraboloid z=x2+y2 and the cylinder x2+y2=1.

Q: Let C be the positively oriented square with vertices (0, 0), (2,0), (2, 2), (0, 2). Use Green's…

A: Let the given square be OABC which is positively oriented.

Q: (a) Find the real and positive constants n and y such that the following velocity field V is…

A: a)    we know that the  velcocity field  is a conservative  if the curl of the velocity field is…

Q: 2: Evaluate the surface integral √√(² + √2 where S is the inverted cone z-1-√√² + y² with z ≥ 0.…

A:

Q: Evaluate the triple integral z dV, where E is enclosed by the paraboloid z= x2 + y2 and the plane…

A:

Q: Evaluate the surface integral. J[x (x + y + z) ds, S is the parallelogram with parametric equations…

A:

Q: Evaluate the triple integral z dV, where E is enclosed by the paraboloid z= 4x2 + 4y2 and the plane…

A:

Q: (x + y + z) ds, S is the parallelogram with parametric equations x = u + v, y = U-v, z = 1+2u+v, 0 ≤…

A: