$\"\"$

The integral is $\"\"$ .

Definition of an improper integral :

If $\"\"$ exists for every number $\"\"$ , then $\"\"$ provoded this limit exists (as a finite number).

The function intervals is undefined at $\"\"$ , so the function is countinous $\"\"$ in the intervals.

$\"\"$

Boundaries : from $\"\"$ to $\"\"$ .

Trigonometric expression is $\"\"$ .

$\"\"$

Therefore, $\"\"$ .

Since $\"\"$ (finite value), the integral is convergent.

$\"\"$

The integral is convergent and the value is $\"\"$ .