$\"\"$

\

The function is $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Hence the function is an odd function.

\

Integral of symmetric functions :

\

Suppose $\"\"$ is continuous on $\"\"$ ,

\

If $\"\"$ is even function i.e $\"\"$ , then $\"\"$ .

\

If $\"\"$ is odd function i.e $\"\"$ , then $\"\"$ .

\

Therefore, from the integral of symmetric functions definition,

\

$\"\"$ .

\

Consider the fact $\"\"$ for all $\"\"$ .

\

Comparision property of definite integrals :

\

If $\"\"$ for $\"\"$ , then $\"\"$ .

\

Here $\"\"$ and $\"\"$ .

\

$\"\"$

\

\

Add $\"\"$ on each side.

\

$\"\"$ $\"\"$

\

$\"\"$ .

\

Hence it is verified.

\

$\"\"$

\

$\"\"$ .