[int_(0)^(16n^(2)/ pi)(cos(pi)/(2)[(x pi)/(n)])dx],[" to "](" where [.] is G.I.F) is equal "

int_(0)^(16n^(2)//pi) "cos" (pi)/(2)[(xpi)/(n)] dx is equal to

int_(0)^(16n^(2)//pi) "cos" (pi)/(2)[(xpi)/(n)] dx is equal to

int_(0)^(16n^(2)//pi) "cos" (pi)/(2)[(xpi)/(n)] dx is equal to

int_(0)^( pi)xf(sin x)dx=(pi)/(2)int_(0)^( pi)f(sin x)dx

The value of int_((pi)/(4))^((pi)/(2))[sin x+[(2x)/(pi)]]dx where [.] denotes G.I.F.

For x in(0, (pi)/(2)) If int(tan x sqrt(sec x)(1+cos^(2)x))/(sqrt(cos x+sin^(2)x))dx=2sqrt(f(x)+1)+c and f((pi)/(3))=(3)/(2) then [f((pi)/(4))] = ( where [.] denotes G.I.F )

int_(-pi//2)^(pi//2)(sin^(2n-1)x)/(1+cos^(2n)x)dx=

If A=int_(0)^( pi)(cos x)/((x+2)^(2))dx, then int_(0)^( pi/2)(sin2x)/(x+1)dx is equal to