Final answer:
To find the volume of the solid region in the first octant bounded by the plane 4x + 8y + 8z = 16 and the coordinate planes, set up a triple integral and evaluate it within the given limits.
Step-by-step explanation:
To find the volume of the solid region in the first octant bounded by the plane 4x + 8y + 8z = 16 and the coordinate planes, we can set up a triple integral. Since the solid is bounded by the coordinate planes, the limits of integration will be 0 to the given values for x, y, and z.
The integral would be:
∫ ∫ ∫ 1 dV
where the limits are:
x: 0 to 4
y: 0 to 2
z: 0 to 2-x/2-y/4
Simplifying this integral will give us the volume of the given solid region.