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

Question

The value of ∫π2 π[2 cos x] d x where [ " ] represents the greatest integer function is (A) -(5 π/6) (B) -(π/2) (C) -π (D) none

Tardigrade Admin · Accepted Answer

Using King I=∫ limitsπ2 π[-2 cos x] d x ; 2 I=∫ limitsπ2 π[2 cos x]+[-2 cos x] d x=(-1)(2 π-π)=-π I=-(π/2)

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