Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the coordinate planes and the plane 2x + y + z = 2

Step-by-step explanation:

Consider the tetrahedron enclosed by the coordinate planes and the plane 2x + y + z = 2

Let A be the region obtained by projecting the volume(V) onto the xy-plane.

Similarly, the plane 2x + y + z = 2 intersects with the xy-plane in y = 2 - 2x.

Using the vertical strips, the region A is to the xy-plane can be expressed as:

Thus, the volume of the solid can be calculated as follows;

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap