Concept explainers
To calculate:
The area of the region enclosed by one loop only:
Explanation of Solution
Given information:
Formula Used:
The formula for the area of the polar region:
Calculation:
The equation of the region is
So, the curve region of
Now, need to find the interval in which the inner loop exists:
That means the area lies between the interval
Since, the curve of the equation is symmetric about the polar axis. Os the area of the loop is gets double between
The area of given equation of the polar region is:
Chapter H.2 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: 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. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning