Integration + Limit

Calculus Level 4

If \( \displaystyle\lim _{ a\rightarrow \pi / 2 ^{ - } }{ \displaystyle \int _{ 0 }^{ a }{ (\cos x)\ln { (\cos x) } dx } } =\ln { (c) } -b\).

Find \(c+b\)


Where \(c\) and \(b\) are natural numbers.

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