The profile of a gear tooth shown in Fig. P9.1 (a) is approximated by the
(a) Estimate the area A using six rectangles of equal width
(b) Calculate the exact area by evaluating the definite
(a)
The estimated area of given function
Answer to Problem 1P
The estimated area of given function by rectangle method is
Explanation of Solution
Given:
The expression of profile of gear tooth is given as:
Number of rectangles given are 6.
Width of the rectangle is given as:
Concept used:
The expression of area is given as:
Here,
Calculation:
For
Substitute
Therefore,
For
Substitute
Therefore,
For
Substitute
Therefore,
For
Substitute
Therefore,
For
Substitute
Therefore,
Substitute
Therefore,
Substitute
Equation (3) can be written as:
Substitute
Conclusion:
Thus, the estimated area of the given function by rectangle method is
(b)
The exact area of given function
Answer to Problem 1P
The exact area of given function by integration method is
Explanation of Solution
Concept used:
The expression of area is given as:
Here,
Calculation:
Substitute
Further simplify for
Conclusion:
Thus, the exact area of given function by integration method is
Want to see more full solutions like this?
Chapter 9 Solutions
Introductory Mathematics for Engineering Applications
Additional Math Textbook Solutions
Basic Technical Mathematics
Fundamentals of Differential Equations (9th Edition)
Advanced Engineering Mathematics
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Elementary Statistics: Picturing the World (6th Edition)
Algebra and Trigonometry
- Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat...Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEY
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,