Final answer:
To find the volume of the region bound underneath the surface z = 4 - x² - y in the first octant, you need to calculate the triple integral of the given function over the specified region using the limits of integration. The volume can be obtained by evaluating the triple integral ∫∫∫ (4-x²-y) dy dx dz over the given limits.
Step-by-step explanation:
To find the volume of the region bound underneath the surface z = 4 - x² - y in the first octant, we need to calculate the triple integral of the given function over the specified region. Since the sides of the region are defined by x = 0, y = 0, and z = 0, the limits of integration for x, y, and z would be 0 to 2, 0 to 2, and 0 to 4-x²-y respectively. The volume can be obtained by evaluating the triple integral ∫∫∫ (4-x²-y) dy dx dz over the given limits.