Final answer:
To set up a triple integral to represent the volume of the ellipsoid, integrate over the region defined by the ellipsoid using the given equation. Determine the limits of integration for each variable and evaluate the triple integral.
Step-by-step explanation:
The equation represents an ellipsoid in three-dimensional space. To set up a triple integral to represent the volume of the ellipsoid, we need to integrate over the region defined by the ellipsoid. In this case, the ellipsoid is given by the equation (u²)/a + (v²)/b + (w²)/c = 1, where a, b, and c are positive numbers representing the semi-axes of the ellipsoid along the u, v, and w directions respectively.
To evaluate the integral, we need to determine the limits of integration for each variable. Since the equation defines the ellipsoid, we need to find the maximum and minimum values of u, v, and w that satisfy the equation. Once we have the limits, we can set up the triple integral as ∫∫∫ dudvdw, where the limits of integration are determined by the maximum and minimum values of u, v, and w.