The average values of a function can be determined by
Use this relationship to verify the results of Eq. (19.13).
To prove: The following results,
If the average value formula is
Explanation of Solution
Given:
The average value formula is
Formula used:
The integral formula are
The trigonometric identity are,
Proof:
Consider the identity,
Use average value formula and take
As it is known that the angular frequency
Therefore,
Use integration formula,
On simplifying further,
Hence, the result is
Now consider next result,
Use average value formula and take
As it is known that the angular frequency
Therefore,
Use the integral formula,
Hence, the result is
Now, consider next result,
Use average value formula and take
As it is known that the angular frequency
Therefore,
Use the trigonometric identity,
Use the integral formula,
Hence, the result is
Now, consider next result,
Use average value formula and take
As it is known that the angular frequency
Therefore,
Use the trigonometric identity,
Use the integral formula,
On further simplifying,
Hence, the result is
Now, consider next result,
Use average value formula and take
As it is known that the angular frequency
Therefore,
Use the trigonometric identity,
On further simplifying,
Hence, the result is
Want to see more full solutions like this?
Chapter 19 Solutions
Numerical Methods for Engineers
- Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.arrow_forwardA soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning