Definite integral Problem-1

Calculus Level 5

If given that 02πdx31+5cosx+6sinx=πa,\displaystyle \int_{0}^{2\pi} \dfrac{dx}{31+5\cos x+6\sin x}=\dfrac{\pi}{a} , find the value of a22.\large \left \lceil \frac{a^2}{2} \right \rceil.

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

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