Express the double integral in terms of a single integral with respect to r. Then use your calculator to evaluate the integral correct to four decimal places.
34. , where D is the portion of the disk x2 + y2 ≤ 1 that lies in the first quadrant
To evaluate: The value of the double integral using calculator.
The function is, .
The region D is the portion of the disk that lies in the first quadrant.
If is a polar rectangle R given by where , then, (1)
If is the function of and is the function of then,
In order to convert the given function into polar coordinates, substitute . Thus, z becomes,
And, from the given region D, r varies from 0 to 1 and varies from 0 to .
Therefore, by the equation (1), the value of the iterated integral becomes,
Integrate the function with respect to r and by using the equation (2).
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started
Single Variable Calculus: Early Transcendentals, Volume I
Precalculus: Mathematics for Calculus (Standalone Book)
Calculus: Early Transcendental Functions
Calculus: An Applied Approach (MindTap Course List)
Finite Mathematics and Applied Calculus (MindTap Course List)
Essentials Of Statistics
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Calculus (MindTap Course List)
Statistics for The Behavioral Sciences (MindTap Course List)
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Single Variable Calculus
Probability and Statistics for Engineering and the Sciences
Understanding Basic Statistics
Elementary Technical Mathematics
Contemporary Mathematics for Business & Consumers
Mathematical Excursions (MindTap Course List)
Mathematical Applications for the Management, Life, and Social Sciences
Elementary Geometry For College Students, 7e
Single Variable Calculus: Early Transcendentals
Calculus of a Single Variable
Calculus: Early Transcendental Functions (MindTap Course List)
Trigonometry (MindTap Course List)
Elements Of Modern Algebra
Study Guide for Stewart's Multivariable Calculus, 8th
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Elementary Geometry for College Students
Finite Mathematics for the Managerial, Life, and Social Sciences