4. Convert the integral from Cartesian coordinates to both cylindrical and spherical coordi- 1-T² rl+ 1-x²-y² nates: 1-x² xdzdydx.

Q: tegral by transforming to polar coordinates.

A:

Q: Parameterize the intersection of z = - Vx² + 7y² _and x² + y? + z? = 200

A:

Q: Evaluate the cylindrical coordinate integrals

A: The given integral is I=∫02π∫03∫r2318-r2dz r dr dθ Solve the innermost integral with respect to r.…

Q: Use spherical coordinates to evaluate 2π FT S 2-r r+z 0 (r² +2²) ³/ rdz dr de.

A:

Q: Q3// B Verify that dv3p'sin Ddpd@d owhen using spherical coordinate

A:

Q: Find and equatin for the parabolid z = x^2+y^2 in spherical coordinates

A: Given query is to find equation of paraboloid in spheo coordinates.

Q: Transform (4, 7/3, ) from spherical into cylindrical form (here o is any angle).

A:

Q: Z x² + z² 2 E = {(x, y, z) | 1 ≤ y ≤ 4, y ≤ z ≤ 4,0 ≤ x ≤ 2} 11. SSSE dV, where

A:

Q: Convert this integral from rectangular coordinates to cylindrical coordinates (Do not evaluate the…

A:

Q: 2. Sketch the cylinder y = x² +1.

A: complete graph provided below with python code Explanation:  code behind above :  import numpy as…

Q: Sketch the cylinder given by x = 4- Z*2（z square）in three-dimensional space.

A: Given: The equation is x=4-z2. To sketch: The given equation in three-dimensional space.

Q: .10π Sr Sa 0 0 (1 - sin o)/2 -л(157-16) A) (1 - cos p)/2 48 5 C) 7(157 - 16) 96 o² sin o do do de 5…

A:

Q: Transform (0, 5, 2) from rectangular into spherical form (here z is any negative number).

A: given rectangular coordinates is of the form (x, y, z) are (0,5,z) Now we are going to find…

Q: Evaluate the cylindrical coordinate integral. 10 20 r 8 dz r dr d0 2 8 0 0 O A. 144 О в. 48 Ос. 96…

A: Solution

Q: Converting into cylindrical coordinates the integral r9-(x²+y²) 9-a2 ydzdrde 9-x2

A:

Q: 1 27 1+sin(0) 2r dr d0 dz -1 0

A:

Q: Question 2 Convert this integral from rectangular coordinates to Cylindrical Coordinates) (do not…

A: Introduction: When we can consider a cylinder within the solid in three-dimensional Euclidean…

Q: Use the cylindrical coordinates to evaluate the triple integral

A:

Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: ܐ 0 √32-x²-y² Se²³+²+² dzdydx ex+y 4-16-xx+y? 0

A: Convert the cartesian coordinates into spherical coordinates.

Q: By changing to spherical coordinate, evaluate (a) z' Vx² + y² +z² dz dy dx (b) " ST* E x² + y° +z?…

A:

Q: Convert S.S. dzdydx 3-√√9-**-* Into an integral of spherical coordinates 319-x2

A:

Q: 4. Let V = R' and let T be the linear operator on V defined by T(1, y, 2, t) = (3t, -y+ 42, 5y, z-…

A: For a finite dimensional vector space V T-cyclic subspace of V generated by v is a subspace {v,…

Q: c) Use spherical coordinate to evaluate V1-x2 1 Vx2 + y? + 22 dz dy dr.

A: The given problem is to evaluate the given triple integral using spherical coordinates, we have to…

Q: Find the Surface area of the portión of the cylinder ya + z² =9 above the rectangle in the xy plane.…

A: Cylinder y2 + z2  = 9,z = 9-y2,0 ≤ x ≤ 2,and-3 ≤ y ≤ 3