Even and odd functions, Mathematics

Assignment Help:

Even and Odd Functions : This is the final topic that we have to discuss in this chapter. 

Firstly, an even function is any function which satisfies,

                                                                f ( x ) = x2

Typical examples of even functions are following,

f ( x ) = f ( x )                                  f ( x ) = cos (x )

An odd function is any function that satisfies,

f (- x ) = - f ( x )

The typical examples of odd functions are following,

f ( x ) = x3                           f (x ) = sin ( x )

There are some nice facts regarding integrating even & odd functions over the interval [-a,a]. If f(x) is an even function then,

a (-a)      f ( x ) dx = 2∫a0 f ( x ) dx

Similarly, if f(x) is an odd function then,

 ∫a (-a)     f ( x ) dx =0

Note as well that in order to use these facts the limit of integration has to be the same number, however opposite signs!


Related Discussions:- Even and odd functions

Oscar sold 2 glasses of milk for each 5 sodas he sold, Oscar sold 2 glasses...

Oscar sold 2 glasses of milk for each 5 sodas he sold. If he sold 10 glasses of milk, how many sodas did he sell? Set up a proportion along with milk/soda = 2/5 = 10x. Cross mu

What is the probability that they will both come to a party, Q.  Suppose th...

Q.  Suppose the probability of David coming to a party is 75% and the probability of Jason coming to a party is 85%. What is the probability that they will both come to a party, a

Integration, why we study integration..?? uses

why we study integration..?? uses

Liner regression, Liner Regression The calculations for our sample siz...

Liner Regression The calculations for our sample size n = 10 are described below. The linear regression model is y = a + bx Table: Distance x miles

Sum of a number of terms in g.p., We know that the terms in G.P. are:...

We know that the terms in G.P. are: a, ar, ar 2 , ar 3 , ar 4 , ................, ar n-1 Let s be the sum of these terms, then s = a + ar + ar 2

Geometry help, One of two complementary angles is 80& of the other. What is...

One of two complementary angles is 80& of the other. What is the degree measure of the smaller angle?

Pumping lemma for context free languages, 1. Construct a grammar G such tha...

1. Construct a grammar G such that L(G) = L(M) where M is the PDA in the previous question. Then show that the word aaaabb is generated by G. 2. Prove, using the Pumping Lemma f

Calculus, Determine the linear approximation for f(x)= sin delta at delta =...

Determine the linear approximation for f(x)= sin delta at delta =0

Shares and dividends, at what price a 6.25%rs 100 share be quoted when the ...

at what price a 6.25%rs 100 share be quoted when the money is worth 5%

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd