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

Linear equation, The ratio between the length and breadth of a rectangular ...

The ratio between the length and breadth of a rectangular field is 11:7. The cost of fencing it is Rs. 75,000. Find the dimensions of the field

Trigonometry, A 25 foot ladder just reaches the top of a house and forms an...

A 25 foot ladder just reaches the top of a house and forms an angle of 41.5 degrees with the wall of the house. How tall is the house?

Highest common factor (hcf), We know that a factor is a quantity whic...

We know that a factor is a quantity which divides the given quantity without leaving any remainder. Similar to LCM above we can find a highest common factor (HCF)

Algebra, solve x+y= 7 and x-y =21

solve x+y= 7 and x-y =21

Properties of dot product - proof, Properties of Dot Product - proof P...

Properties of Dot Product - proof Proof of: If v → • v → = 0 then v → = 0 → This is a pretty simple proof.  Let us start with v → = (v1 , v2 ,.... , vn) a

What is the new cost of the pants, A pair of pants costs $24. The cost was ...

A pair of pants costs $24. The cost was decreased by 8%. What is the new cost of the pants? If the cost of the pants is decreased by 8%, the cost of the pants is 92 percent of

Relationship between the entries of a rotation matrix, 1. A 3d rotation mat...

1. A 3d rotation matrix has 9 (3 by 3) entries, and a 2d rotation matrix has 4 (2 by 2) entries. How many actual degrees of freedom are there in a 3d or 2d rotation? In other words

Dividing, If I divide any number do I get the manservant 2 times

If I divide any number do I get the manservant 2 times

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