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Evaluate
Solution:
Consider the given equation above
Integrate the given equation first with respect to z. Consider x and y are constants
Next, integrate the equation above with respect to y. Consider x as a constant, we have
The integral of zero with respect to any variable is always equal to a constant. At the above equation, we cannot substitute the value of the limits because there's no variable present in the equation.
Therefore,
Did you notice that if the limits for the second integration is from - x to x, the value of definite integral will be equal to zero? In this case, the function or curve is symmetrical to y-axis. We can rewrite the second integration as follows
or
Use the second equation above so that it is easier for us to integrate the equation, we have
Therefore,
