Final answer:
The solution involves calculating a triple integral of ex over a given volume by integrating step-by-step concerning z, x, and then y within the given limits.
Step-by-step explanation:
The question asks us to evaluate a triple integral of the function ex over a specified volume. Since the limits for y, x, and z have been provided, we can set up the integral accordingly. The general approach to solving a triple integral is to perform the integration in steps, solving one integral at a time. We start by integrating concerning z, followed by x, and finally y.
First, we integrate concerning z from 0 to 4y, keeping in mind that x and y are constants for this integral. After that, we integrate the resulting expression concerning x from 0 to √(4-y²). Lastly, we integrate concerning y from 0 to 2. The exact calculations are not provided, but the student is guided on the method to be used for the solution.
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