Concept explainers
To evaluate: The integral function
Answer to Problem 60E
The evaluation of the integral is
Explanation of Solution
Given:
The integral function is
The region lies between
The substitution is
Calculation:
Consider
Differentiate both sides of the Equation (1).
Calculate the lower limit value of u using Equation (1).
Substitute 0 for x in Equation (1).
Calculate the upper limit value of u using Equation (1).
Substitute 1 for x in Equation (1).
The integral function is,
Apply lower and upper limits for u in Equation (2).
Substitute u for
Interpret the integral function.as the area of a quarter-circle with radius 1.
The integral function (I) equals to the area of a quarter-circle with radius 1.
Modify Equation (3) as follows:
Hence, the evaluation of the integral is
Chapter 5 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