Teach me this, I want to fully understand it! The best way possible! Below is the transcribed mathematical expression suitable for an educational website:\[ 2. \int_{1}^{2} \int_{3}^{4} \sqrt{xy} \, dy \, dx = \int_{1}^{2} \sqrt{x} \, dx \int_{3}^{4} \sqrt{y} \, dy \] ### Explanation:This expression represents the equality of two iterated integrals. The left side involves integrating the function \(\sqrt{xy}\) first with respect to \(y\) from 3 to 4, and then with respect to \(x\) from 1 to 2. The right side separates the integration into a product of two integrals: one for \(\sqrt{x}\) with respect to \(x\) from 1 to 2, and the other for \(\sqrt{y}\) with respect to \(y\) from 3 to 4.This equality demonstrates how the integration of a function of two variables can sometimes be separated into simpler integrals when the function can be expressed as a product of single-variable functions.

Answered: Image /qna-images/answer/2e5d7e5a-b3be-48c0-ba88-4c7df00a7c29.jpg

Answered: 2. ₁²√xydydx = ²√xdx √ydy

2. ₁²√xydydx = ²√xdx √ydy

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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