$\"\"$

\

The integral expression is $\"\"$ .

\

Theorem :

\

If $\"\"$ is integrable on $\"\"$ , then $\"\"$ ,

\

where width of the interval $\"\"$ and $\"\"$ .

\

The integral expression is $\"\"$ .

\

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

\

width of the interval :

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Sum of first $\"\"$ natural numbers is $\"\"$ .

\

Sum of the squares of first $\"\"$ natural numbers is $\"\"$ .

\

Simplify the expression.

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ .