int_(0)^(2 pi)[2sin x]dx=

The value of int_0^(2pi)[2 sin x] dx , where [.] represents the greatest integral functions, is

The value of int_0^(2pi)[2 sin x] dx , where [.] represents the greatest integral functions, is

int_0^(2pi) sin^2x dx

Prove the equality int_(0)^(pi) f (sin x) dx = 2 int_(0)^(pi//2) f (sin x) dx

Compute the integrals : (a) int_(0)^(pi//2) sin 2x dx , (b) int_(pi//6)^(pi//2) (cos x)/(sin^(3) x) dx (c) int_(0)^(1) (dx)/( sqrt(16 - x^(2)))

If I=int_(0)^(2pi) sin^(2) x" dx" , then

int _(0) ^(2pi) ( sin 2x )dx