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Evaluate the iterated integral. Integral from 0 to 3 integral from 0 to 1 integral from 0 to...

Question:

Evaluate the iterated integral.

{eq}\int_{0}^{3} \int_{0}^{1} \int_{0}^{\sqrt{1 - z^2}} 22ze^y \, \mathrm{d}x \, \mathrm{d}z \, \mathrm{d}y {/eq}

Iterated Integral

An iterated integral is an integration operation that contains multiple and successive integrals. The function being integrated is usually a multivariate function. To evaluate an iterated integral, start by integrating with respect to the innermost differential while treating all other variables as a constant.

Answer and Explanation: 1

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The given iterated integral is:

{eq}\begin{align*} \int_0^3 \int_0^1 \int_0^{\sqrt{1-z^2}} 22ze^y \,dx\,dz\,dy \end{align*} {/eq}

Since...

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Double Integrals & Evaluation by Iterated Integrals

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Chapter 15 / Lesson 4
633

In this lesson, we show how to evaluate a double integral using iterative integration. A special case is also presented which simplifies the calculations.


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