Question

Evaluate the triple integral ∭Tx2dV, where T is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,3,0), and (0,0,3).

Answer 1

To evaluate the triple integral ∭Tx²dV, we need to integrate over the solid tetrahedron T defined by the vertices (0,0,0), (3,0,0), (0,3,0), and (0,0,3).

Step-by-step explanation:

To evaluate the triple integral ∭Tx²dV, we need to integrate over the solid tetrahedron T defined by the vertices (0,0,0), (3,0,0), (0,3,0), and (0,0,3). Since T is a three-dimensional shape, we need to perform a triple integral.

The limits of integration for each variable are as follows:

x: 0 to 3-y-z

y: 0 to 3-z

z: 0 to 3

Substituting the limits into the integrand Tx², we can then evaluate the triple integral by integrating with respect to x, y, and z in the given limits.