Find the volume of a parallelepiped if four of its eight
vertices area ? = (0,0,0),...
Find the volume of a parallelepiped if four of its eight
vertices area ? = (0,0,0), ? = (1,0,2), ? = (0,2,1), ? =
(3,4,0).
a) Find the volume of the region bounded by Z = (X2 +
Y2)2 and Z...
a) Find the volume of the region bounded by Z = (X2 +
Y2)2 and Z = 8 (Show all steps)
b) Find the surface area of the portion of the surface z =
X2 + Y2 which is inside the cylinder
X2 + Y2 = 2
c) Find the surface area of the portion of the graph Z = 6X + 8Y
which is above the triangle in the XY plane with vertices (0,0,0),
(2,0,0), (0,4,0)
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.
Find the volume under the plane 2x − 3y + 4z = 32 above the
triangle...
Find the volume under the plane 2x − 3y + 4z = 32 above the
triangle with vertices (1,0,0), (0,0,0), and (0,4,0).
Find the volume of the tetrahedron whose vertices are P(1,2,3),
Q(2,4,6), R(2,3,4,), and S(4,1,5)
Find the volume of the tetrahedron whose vertices are P(1,2,3),
Q(2,4,6), R(2,3,4,), and S(4,1,5)
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