A calculus problem by Akshat Sharma

Calculus Level 5

\(\int _{ 0 }^{ \pi /2 }{ \frac { cos(x) }{ (A)cos(x)+(B)sin(x) } } \)

where,

A= \(\left\lfloor { \pi }^{ 2 }\int _{ \pi /4 }^{ \pi /3 }{ \frac { sin(x) }{ x } } \right\rfloor\)

B=\(16\left\{ \sum _{ r=0 }^{ n }{ \left( { (-1) }^{ r } \right) \frac { \left( \begin{matrix} n \\ r \end{matrix} \right) }{ \left( \begin{matrix} r+3 \\ r \end{matrix} \right) } } ,where\quad n=9 \right\}\)

{ } is not fractional part.

Answer to 3 decimal digits.

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