Change the order of integration, but do not evaluate, the following integrals: a....

Question:

Change the order of integration, but do not evaluate, the following integrals:

a. {eq}\int_{0}^{8}\int_{\frac{1}{2y}}^{4}dx\;dy {/eq}

b. {eq}\int_{0}^{9}\int_{0}^{\sqrt{y}}dx\;dy {/eq}

c. {eq}\int_{0}^{4}\int_{-\sqrt{16-y^2}}^{\sqrt{16-y^2}}dx\;dy {/eq}

d. {eq}\int_{\frac{\pi}{2}}^{\pi}\int_{0}^{sin\;x}dy\;dx {/eq}

Double Integral

We will reverse the order of integration where we will find the limits whose another variable will be constant and then after solving the integral we will plug-in the bounds.

Answer and Explanation: 1

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a) To solve the problem we will reverse the order of integration:

{eq}\int_{0}^{4}\int_{\frac{1}{2x}}^{8}dydx {/eq}

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Double Integrals: Applications & Examples

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Chapter 12 / Lesson 14
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Double integrals extend the possibilities of one-dimensional integration. In this lesson, we will focus on the application of the double integral for finding enclosed area, volume under a surface, mass specified with a surface density, first and second moments, and the center of mass.


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