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  4. The value of ∫π2 π[2 cos x] d x where [ ] represents the greatest integer function is

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Q. The value of $\int_\pi^{2 \pi}[2 \cos x] d x$ where [ " ] represents the greatest integer function is

Integrals

Solution:

Using King
$I=\int\limits_\pi^{2 \pi}[-2 \cos x] d x ; 2 I=\int\limits_\pi^{2 \pi}[2 \cos x]+[-2 \cos x] d x=(-1)(2 \pi-\pi)=-\pi $
$I=-\frac{\pi}{2}$