Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Related questions
Question
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.](https://content.bartleby.com/qna-images/question/76c78a43-228d-485d-a6cf-d30956c84b3b/2e5d7e5a-b3be-48c0-ba88-4c7df00a7c29/9rejszm_processed.jpeg)
Transcribed Image Text: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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 3 steps with 3 images
Knowledge Booster
Similar questions
- not sure where I'm going wrong..arrow_forwardCan you help me please! How did the mathematical concepts that developed during Arabic period have an impact on modern mathematics? Discuss the cultural and historical setting during Arabic period.arrow_forwardI don't understand that question can you help mearrow_forward
- What is an example of something going on in your mind or body that is automatically controlled by math or has a math equation that goes with it?arrow_forwardcan you help me with this exercise from A to I pleasearrow_forwardI am only needing help on the second picture I can not figure out how to simply this.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage Learning
Thomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSON
Calculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON 
Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. Freeman
Calculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning