`int_(-pi/3)^0[cot^(-1)(2/(2cosx-1))+cot^(-1)(cosx-1/2)]dx` i s equal to (a)`(pi^2)/6` (b) `(pi^2)/3` (c) `(pi^2)/8` (d) `(3pi^2)/8`

int_0^pi(xtanx)/(secx+cosx)dxi s (pi^2)/4 (b) (pi^2)/2 (c) (3pi^2)/2 (d) (pi^2)/3

int_(5/2)^5(sqrt((25-x^2)^3))/(x^4)dx is equal to (a) pi/6 (b) (2pi)/3 (c) (5pi)/6 (d) pi/3

cot((pi)/(4)-2cot^(-1)3)

int_(0)^(pi)|cosx|^(3) dx is equal to (a) (4)/(3) (b) (2)/(3) (c) 0 (d) (-8)/(3)

The value of int_(-pi//2)^(pi//2)(x^(2)cosx)/(1+e^(x)) d x is equal to

IfA=int_0^pi(cosx)/((x+2)^2)dx ,t h e nint_0^(pi/2)(sin2x)/(x+1)dx is equal to (a) 1/2+1/(pi+2)-A (b) 1/(pi+2)-A (c) 1+1/(pi+2)-A (d) A-1/2-1/(pi+2)

One of the root equation cosx-x+1/2=0 lies in the interval (a) (0,pi/2) (b) (-pi/(2,0)) (c) (pi/2,pi) (d) (pi,(3pi)/2)

The value of sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))), where x in (pi/2,pi) , is equal to (a) pi/2 (b) -pi (c) pi (d) -pi/2

The value of cos^(-1)sqrt(2/3)-cos^(-1)((sqrt(6)+1)/(2sqrt(3))) is equal to (A) pi/3 (B) pi/4 (C) pi/2 (D) pi/6

int_(-(pi)/(2))^((pi)/(2))(sin^3xdx)/(1+cosx)= .