(a)
To find: The area of
(a)
Answer to Problem 53RE
The area of
Explanation of Solution
Given:
The equation of the polar curve is defined by
Calculation:
The area of the region for the polar curve is given by,
Find the area of
Therefore, the area of
(b)
To convert: The polar equation to rectangular coordinates and proves that the curves are the same.
(b)
Answer to Problem 53RE
It is proved that the curve is same.
Explanation of Solution
Given:
The equation of the parabola is
Calculation:
To convert the given polar equation into an equivalent Cartesian equation, use the various mathematical operations and the Polar-Rectangular Cartesian formulas which are,
Consider
It is known that
Therefore, it is proved that the curve is same.
(c)
To set: The integral in rectangular coordinates that gives the area of
(c)
Answer to Problem 53RE
The integral in rectangular coordinates that gives the area of
Explanation of Solution
Given:
The equation of the parabola is
Calculation:
The Cartesian form of the curve is,
To find the limits substitute
So, the integral in rectangular coordinates that gives the area of
Therefore, the integral in rectangular coordinates that gives the area of
Chapter 11 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
Additional Math Textbook Solutions
Calculus & Its Applications (14th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th 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