# Definite integral Problem-1

Calculus Level 5

If given that $\displaystyle \int_{0}^{2\pi} \dfrac{dx}{31+5\cos x+6\sin x}=\dfrac{\pi}{a} ,$ find the value of $\large \left \lceil \frac{a^2}{2} \right \rceil.$

Clarification: $$\lceil .. \rceil$$ denotes ceiling function.

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