Paneer Definite Masala 10

Calculus Level 5

\[ \large I_1 =\int_0^\pi \text{sinc}(x) \, dx \qquad I_2 = \int_0^{\pi /2} \text{sinc}(x) \text{sinc} \left( \dfrac\pi2 - x\right) \, dx \]

\(I_1\) and \(I_2\) are two definite integrals as described above and \(\dfrac{I_1}{I_2} = \dfrac {A\pi^B}C \), where \(A\), \(B\) and \(C\) are positive integers, find \(A+B+C\).

Notation: \(\text{sinc}(x) = \dfrac{\sin x}x \) denotes the sinc function.

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