# MATH = Mental Abuse To Humans

Calculus Level 5

$\int^{\pi /2}_0 (\sin{x}+a\cos{x})^3\,dx - \dfrac{4a}{\pi-2} \int^{\pi /2 }_0 x\cos{x} \,dx = 2$

If $$a_1, a_2$$ and $$a_3$$ are the three values of $$a$$ which satisfy the equation above, then find the value of $$1000 \left(a^2_1+a^2_2+a^2_3\right)$$.

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