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

The mean value theorem for integrals of even and odd , The Mean Value Theor...

The Mean Value Theorem for Integrals If  f (x ) is a continuous function on [a,b] then there is a number c in [a,b] such as,                                    ∫ b a f ( x

Adding equally sized groups-prerequisites for multiplication, Adding Equall...

Adding Equally Sized Groups:  Once children have had enough practice of making groups of equal size, you can ask them to add some of these equal groups. They can now begin to atte

Number line, I need to graph rational numbers on the number line Point A-.6...

I need to graph rational numbers on the number line Point A-.60, point B-1/4, point C-.4,point D-7/8

Airthmetic progression series, Each of the series 3+5+7+..... and 4+7+10......

Each of the series 3+5+7+..... and 4+7+10.......... is continued to 100 terms find how many terms are identical. Ans) 48 terms would be common to both the series... first take co

Circles, If the distances from origin of the centres of 3 circles x 2 +y 2 ...

If the distances from origin of the centres of 3 circles x 2 +y 2 +2alphaix= a 2 (i=1,2,3) are in G.P. , then length of the tangents drawn to them frm any point on the circles x2+

Fractions, what Is the common denominator for 1/2 and 1/4

what Is the common denominator for 1/2 and 1/4

Geometry, finding missing values from given triangle diagra m..

finding missing values from given triangle diagra m..

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