Evaluating Triple Integrals over Boxes Examples 1
Recall from the Fubini’s Theorem for Evaluating Triple Integrals over Boxes page that if $w = f(x, y, z)$ is a three variable real-valued functions and $f$ is continuous over the box $B = [a, b] \times [c, d] \times [r, s]$, then the triple integral of $f$ over the box $B$ can be evaluated as iterated integrals:
Let’s look at some examples of evaluating triple integrals over boxes.
Evaluate the triple integral $\iiint_B 2x + 3y + 4z \: dV$ where $B = [0, 1] \times [0, 2] \times [0, 3]$.
We immediately set up our triple integral as iterated integrals and evaluate:
Evaluate the triple integral $\iiint_B xye^x \: dV$ where $B = [0, 1] \times [0, 2] \times [0, 1]$.
We immediately set up our triple integral as iterated integrals and evaluate.
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