Chapter 13: Q. 52 (page 1056)

In Exercises 45–52, rewrite the indicated integral with the specified order of integration.
Exercise 42 with the order dy dx dz.

Short Answer

Expert verified

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

Step by step solution

Step 1. Given Information.

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

Step 2. Rewrite the integral.

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

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

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

The limit ofxalters from $- 3 to 3 .$

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

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

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In Exercises 45–52, rewrite the indicated integral with the specified order of integration.
Exercise 42 with the order dy dx dz.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Rewrite the integral.

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In Exercises 45–52, rewrite the indicated integral with the specified order of integration.Exercise 42 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

Applied Mathematics

Mechanics Maths

Logic and Functions

Probability and Statistics

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

In Exercises 45–52, rewrite the indicated integral with the specified order of integration.
Exercise 42 with the order dy dx dz.