# 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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