Homework Help is Here – Start Your Trial Now!
Math
Calculus
Describe the domain of integration of the integral. [² √81-x² /81-x²-² xy dz dy dx Choose the inequalities which describe the domain. x2 - y² x2 ) 0 ≤ x ≤ 9,0 ≤ y ≤ √√81 - x²,0 ≤ z ≤ √√√81 00≤x≤ √√81 - x² - y²,0 ≤ y ≤ 9,0 ≤ z ≤ √81 00≤x≤ 9,0 ≤ y ≤ √√81 - x² - y²,0 ≤ z ≤ √√81 - x² 00≤x≤ √√81-x²,0 ≤ y ≤ 9,0 ≤ z ≤ √√81 x² - y²

Describe the domain of integration of the integral. [² √81-x² /81-x²-² xy dz dy dx Choose the inequalities which describe the domain. x2 - y² x2 ) 0 ≤ x ≤ 9,0 ≤ y ≤ √√81 - x²,0 ≤ z ≤ √√√81 00≤x≤ √√81 - x² - y²,0 ≤ y ≤ 9,0 ≤ z ≤ √81 00≤x≤ 9,0 ≤ y ≤ √√81 - x² - y²,0 ≤ z ≤ √√81 - x² 00≤x≤ √√81-x²,0 ≤ y ≤ 9,0 ≤ z ≤ √√81 x² - y²

Calculus: Early Transcendentals
Calculus: Early Transcendentals
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...
See similar textbooks
Question
**Evaluate the Integral** (Use symbolic notation and fractions where needed.) \[ \int_{0}^{9} \int_{0}^{\sqrt{81-x^2}} \int_{0}^{\sqrt{81-x^2-y^2}} xyz \, dz \, dy \, dx = \text{[Answer]} \] This problem involves a triple integral, which calculates the volume under the surface defined by the function \(xyz\) over the given region. The limits describe a portion of a sphere of radius 9, as indicated by the square roots in the limits of integration. The integration is conducted in the order \(dz \, dy \, dx\).
Transcribed Image Text:**Evaluate the Integral** (Use symbolic notation and fractions where needed.) \[ \int_{0}^{9} \int_{0}^{\sqrt{81-x^2}} \int_{0}^{\sqrt{81-x^2-y^2}} xyz \, dz \, dy \, dx = \text{[Answer]} \] This problem involves a triple integral, which calculates the volume under the surface defined by the function \(xyz\) over the given region. The limits describe a portion of a sphere of radius 9, as indicated by the square roots in the limits of integration. The integration is conducted in the order \(dz \, dy \, dx\).
**Describe the domain of integration of the integral.** \[ \int_0^9 \int_0^{\sqrt{81-x^2}} \int_0^{\sqrt{81-x^2-y^2}} xyz \, dz \, dy \, dx \] **Choose the inequalities which describe the domain.** - ○ \(0 \leq x \leq 9, \, 0 \leq y \leq \sqrt{81-x^2}, \, 0 \leq z \leq \sqrt{81-x^2-y^2}\) - ○ \(0 \leq x \leq \sqrt{81-x^2-y^2}, \, 0 \leq y \leq 9, \, 0 \leq z \leq \sqrt{81-x^2}\) - ○ \(0 \leq x \leq 9, \, 0 \leq y \leq \sqrt{81-x^2-y^2}, \, 0 \leq z \leq \sqrt{81-x^2}\) - ○ \(0 \leq x \leq \sqrt{81-x^2}, \, 0 \leq y \leq 9, \, 0 \leq z \leq \sqrt{81-x^2-y^2}\)
Transcribed Image Text:**Describe the domain of integration of the integral.** \[ \int_0^9 \int_0^{\sqrt{81-x^2}} \int_0^{\sqrt{81-x^2-y^2}} xyz \, dz \, dy \, dx \] **Choose the inequalities which describe the domain.** - ○ \(0 \leq x \leq 9, \, 0 \leq y \leq \sqrt{81-x^2}, \, 0 \leq z \leq \sqrt{81-x^2-y^2}\) - ○ \(0 \leq x \leq \sqrt{81-x^2-y^2}, \, 0 \leq y \leq 9, \, 0 \leq z \leq \sqrt{81-x^2}\) - ○ \(0 \leq x \leq 9, \, 0 \leq y \leq \sqrt{81-x^2-y^2}, \, 0 \leq z \leq \sqrt{81-x^2}\) - ○ \(0 \leq x \leq \sqrt{81-x^2}, \, 0 \leq y \leq 9, \, 0 \leq z \leq \sqrt{81-x^2-y^2}\)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
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: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS