3. Express the integral I = f(x, yz) dV as an iterated integral in three different ways, where E E is the part of the spherical solid x² + y² + z² ≤ a² in the first octant. (a) In rectangular coordinates dz dy dx. (b) In cylindrical coordinates dz dr de. (c) In spherical coordinates dr do do.

Q: Compute the differential of surface area for the surface S described by the given parametrization.…

A: Given that we need to determine the differential of surface area using above parametriation.

Q: 2. Given F(x, y, z) = -y²ī+ xj + z²k and the curve C, intersection of the plane y + z = 3 and the…

A: Given that F→(x, y, z)=-y2i+xj+z2k and the curve C, intersection of the plane y+z=3  and the…

Q: Write a triple iterated integral in cylindrical coordinates (dzdrdtheta) and solve

A:

Q: Use cylindrical coordinates to evaluate d V when

A: The given integral is ∭RxdV where the region R is defined by R:x2+y2≤1, x≥0, y≥0, 0≤z≤2. Converting…

Q: luate the surface integral. // (x + y + z) ds, S is the parallelogram with parametric equations x =…

A: Sub x= u+v  y= u-v  z= 1+2u+v

Q: (xy + z) dz dx dy into an integral in cylindrical coordinates. Convert the integral (D); ,(0). (O)…

A:

Q: 3. (15 pants) Evaluate the line integral Y ds where C is part of the parabola y = x² from (0,0) to…

A:

Q: Use spherical coordinates to find [[[, z2 dV.

A: In this question, we find the triple integral by using spherical coordinate with a sketch of solids

Q: Evaluate the integral by changing to cylindrical coordinates. V 16 - x2 16 - x2 - y2 x² + y? dz dy…

A:

Q: 2. Evaluate the integral by first converting into spherical coordinates: a-y (a2-y2 a--y a2-x2-y2…

A:

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

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:

Q: Use Stokes' Theorem to evaluate // (V x F) · dS where M is the hemisphere x? + y + z? = 9, x > 0,…

A:

Q: Use spherical coordinates to evaluate the triple integral SSSE x2 + y2 + z2 dV, Where E is the ball:…

A: Use spherical coordinates to evaluate the triple integral SSSE x2 + y2 + z2 dV, Where E is the ball:…