Chapter 13: Q. 51 (page 1056)

In Exercises 45–52, rewrite the indicated integral with the specified order of integration.
Exercise 41 with the order dy dx dz.

Short Answer

Expert verified

The given indicated integral with the specified order of integration is $\int_{- 3}^{3} \int_{- \sqrt{9 - z^{2}}}^{\sqrt{9 - z^{2}}} \int_{- \sqrt{9 - x^{2} - z^{2}}}^{\sqrt{9 - x^{2} - z^{2}}} f (x, y, z) d y d x d z .$

Step by step solution

Step 1. Given Information.

The given triple integral is $\int_{- 3}^{3} \int_{- \sqrt{9 - x^{2}}}^{\sqrt{9 - x^{2}}} \int_{- \sqrt{9 - x^{2} - y^{2}}}^{\sqrt{9 - x^{2} - y^{2}}} f (x, y, z) d z d y d x .$

Step 2. Rewrite the integral.

We have to write the given integral in order of dy dx dz.

So, the limit of the integration will vary as follows:

The limit of y alters from $- \sqrt{9 - x^{2} - z^{2}} to \sqrt{9 - x^{2} - z^{2}} .$

The limit of xalters from $- \sqrt{9 - z^{2}} to \sqrt{9 - z^{2}} .$

The limit of zalters from $- 3 to 3 .$

Hence the indicated integral with the specified order of integration is $\int_{- 3}^{3} \int_{- \sqrt{9 - z^{2}}}^{\sqrt{9 - z^{2}}} \int_{- \sqrt{9 - x^{2} - z^{2}}}^{\sqrt{9 - x^{2} - z^{2}}} f (x, y, z) d y d x d z .$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In Exercises 45–52, rewrite the indicated integral with the specified order of integration.
Exercise 41 with the order dy dx dz.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Rewrite the integral.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Geometry

Statistics

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In Exercises 45–52, rewrite the indicated integral with the specified order of integration.Exercise 41 with the order dy dx dz.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Rewrite the integral.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Geometry

Statistics

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In Exercises 45–52, rewrite the indicated integral with the specified order of integration.
Exercise 41 with the order dy dx dz.