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

Probabily example, A sample of students had a mean age of 35 years along w...

A sample of students had a mean age of 35 years along with a standard deviation of 5 years. A student was randomly picked from a group of 200 students. Determine the probability

Explain histogramsin details, Explain Histogramsin details? Another way...

Explain Histogramsin details? Another way to display frequencies is by using a histogram. The following is an example of a histogram using the data from the previous example:

Positive integer, (a)   Specify that  the sum of  the degrees  of all verti...

(a)   Specify that  the sum of  the degrees  of all vertices of a graph  is double the number of edges  in  the graph.                            (b)  Let G be a non directed gra

Pert, define algorithm of pert and pert with suitable examples

define algorithm of pert and pert with suitable examples

The limit, The Limit : In the earlier section we looked at some problems ...

The Limit : In the earlier section we looked at some problems & in both problems we had a function (slope in the tangent problem case & average rate of change in the rate of chan

Factor, 27-125 a power -135a +225a power2

27-125 a power -135a +225a power2

Advanced functions, writ the equation that describes the motion of a point ...

writ the equation that describes the motion of a point on the wheel that has a center of 4m off the ground, has radius of 15 cm, makes a full rotation every 10 seconds and starts a

Lim.., how can solve limits

how can solve limits

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