The tetrahedron is the first octant bounded by the coordinate
planes and the plane passing through...
The tetrahedron is the first octant bounded by the coordinate
planes and the plane passing through (1,0,0), (0,2,0), and
(0,0,3).
I need to calculate the volume of this region, how should this
be done?
6. Let R be the tetrahedron in the first octant bounded by the
coordinate planes and...
6. Let R be the tetrahedron in the first octant bounded by the
coordinate planes and the plane passing through (1, 0, 0), (0, 1,
0), and (0, 0, 2) with equation 2x + 2y + z = 2, as shown below.
Using rectangular coordinates, set up the triple integral to find
the volume of R in each of the two following variable orders, but
DO NOT EVALUATE.
(a) triple integral 1 dxdydz
(b) triple integral of 1 dzdydx
a) Sketch the solid in the first octant bounded by:
z = x^2 + y^2 and...
a) Sketch the solid in the first octant bounded by:
z = x^2 + y^2 and x^2 + y^2 = 1,
b) Given
the volume density which is proportional to the distance from the
xz-plane, set up integrals
for finding the
mass of the solid using cylindrical
coordinates, and spherical coordinates.
c) Evaluate one of these to find the mass.
B is the solid occupying the region of the space in the first
octant and bounded...
B is the solid occupying the region of the space in the first
octant and bounded by the paraboloid z = x2 + y2- 1 and the planes
z = 0, z = 1, x = 0 and y = 0. The density of B is proportional to
the distance at the plane of (x, y).
Determine the coordinates of the mass centre of solid B.
A solid Tetrahedron has vertices (0, 0, 0), (2, 0, 0), (0, 4,
0), and (0,...
A solid Tetrahedron has vertices (0, 0, 0), (2, 0, 0), (0, 4,
0), and (0, 0, 6).
(a) i. Sketch the tetrahedron in the xyz-space.
ii. Sketch (and shade) the region of integration in the
xy-plane.
(b) Setup one double integral that expresses the volume of the
tetrahedron. Define the proper limits of integration and the order
of integration. DO NOT EVALUATE.