Mind explosion!

Calculus Level 2

a = 2011+t2dt\large \sqrt{\color{#D61F06}{a}} ~=~ \sqrt { 2 } \sqrt { \int _{ 0 }^{ \infty }{ \frac { 1 }{ 1+{ t }^{ 2 } } } dt }

alogπ2 = ?\huge \color{#D61F06}{a}^{\log _{ \pi }{ 2 } } ~=~?

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