The region is a right circular cone, 2 = Var? + y2 with height 29. Find the limits of integration on the triple integral for the volume of the cone using Cartesian, cylindrical, and spherical coordinates and the function to be integrated. For your answers 0 theta, o=phi, and p = rho. Cartesian V = p(x, y, z) dz dy da where A C = B = ,F= E ,D= and p(x, y, z) = Cylindrical V = so" C"S"...
The region is a right circular cylinder of radius 2, with the bottom at -5 and top at 5. Find the limits of integration on the triple integral for the volume of the cylinder using Cartesian, cylindrical, and spherical coordinates and the function to be integrated. For your answers 8 theta, o =phi, and prho. Cartesian v=1" / ")*P(2,9,2) dyde de where A= -2 B= 2 E = -5 -sqrt(4-x^2) D= sqrt(4-x^2) and p(x, y, z) = F = 5...
(9 points) Suppose f(x, y, z) = - and D is the domain inside the sphere x2 + y2 + z2 x2 + y2 + z2 = 1 and outside the cone za Enter p as rho, as phi, and as theta. As an iterated integral, BRD (F sav = SITE dp do do JA JC JE with limits of integration
(1 point) The region W is the cone shown below. The angle at the vertex is #/3, and the top is flat and at a height of 3v3. Write the limits of integration for wdV in the following coordinates (do not reduce the domain of integration by taking advantage of symmetry): (a) Cartesian: With a = .b = .d = and f = e = Volume = / ddd (b) Cylindrical: With a = CE and f = ddd e...
(z2 + y*) dV where D is the region inside the cone z- V z2 +アbelow the plane z = 3, and inside the first ai 1- octant z 2 0,y 2 0,z2 0 (z2 + y*) dV where D is the region inside the cone z- V z2 +アbelow the plane z = 3, and inside the first ai 1- octant z 2 0,y 2 0,z2 0
5a. The solid E lies above the cone z =V3V2 + y and below the sphere cº + y2 + 2 = 9. Completely set up, but DO NOT EVALUATE, the triple integral Ssse (y+z)dV in spherical coordinates. Show appropriate work for obtaining the limits of integration and include a sketch. Your answer should be completely ready to evaluate. (9 points) 5b. Completely set up, but DO NOT EVALUATE, the same triple integral ple (y + x)2V from part (a),...
Consider the triple integral SISE g(x,y,z)d), where E is the solid bounded above by the sphere x2 + y2 + z2 = 18 and below by the cone z? = x2 + y2. a) Set up the triple integral in rectangular coordinates (x,y,z). b) Set up the triple integral in cylindrical coordinates (r, 0,z). c) Set up the triple integral in spherical coordinates (2,0,0).
(1 point) The region W is the cone shown below. C The angle at the vertex is /2, and the top is flat and at a height of 5 Write the limits of integration for f dV in the following coordinates (do not reduce the domain of integration by taking advantage of symmetry) (a) Cartesian: With a b d and f eb d Volume (b) Cylindrical: With a= b d and f eb ed f d Volume = (c) Spherical:...
please show all work in clean and legible handwriting with all labels and steps that is properly explained for PROBLEMS #1, 2, 3, AND 4. Any incorrect answers and not solving all 4 problems will get an immediate thumbs down because they did not follow directions, thank you 1) Express the triple integral Ⅲf (x,y,z) dV as an iterated integral in the two a) E={(x,y,z)Wr2+yszaj orders dzdy dr and dz dr dy where b) Sketch the solid region E c)...
(1 point) The region W is the cone shown below. The angle at the vertex is T/3, and the top is flat and at a height of 3V3. 09 Jw dV in the following coordinates (do not reduce the domain of integration by taking advantage of Write the limits of integration for symmetry) (a) Cartesian With a- , and f - e- - o e la Volume Ja Jc Je (b) Cylindrical With a- cz , and f - e-...