## Differrentiating and Integrating Odd and Even Functions

The condition for functions to be odd or even are\[f(x)=-f(-x)\]

\[f(x)=f(-x)\]

respectively.

When you differentiate these equations you get

\[f'(x)=--f'(-x)=f'(-x)\]

(1)\[f'(x)=-f'(-x)\]

(2)Differentiating an odd function gives an even function and vice versa. The same is not true when integrating in general, because of the role of the arbitrary constant .Integrating(1)and(2)gives

\[f(x)=-f(-x)+c\]

\[f(x)=f(-x)+c\]

so the odd and even conditions fail without the further condition that

\[c=0\]

.