Question

Evaluate the triple integral SSS(T) x² dv, where T is the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,1,0) and (0,0,1)

Answer 1

To evaluate the triple integral of x² over the tetrahedron T, we can break it down into three separate integrals with respect to the x, y, and z-coordinates. The limits of integration for each integral are defined by the dimensions of the tetrahedron.

Step-by-step explanation:

To evaluate the triple integral of x² over the tetrahedron T, we can break it down into three separate integrals.

Let's use a Cartesian coordinate system to represent the tetrahedron.

The first integral will be with respect to the x-coordinate, and the limits of integration will be from 0 to 1.

The second integral will be with respect to the y-coordinate, and the limits of integration will be from 0 to 1-x.

The third integral will be with respect to the z-coordinate, and the limits of integration will be from 0 to 1-x-y.

The result of these three integrals will give us the value of the triple integral.