If `int_0^1(sint)/(1+t)dx=alpha,` then the value of the integral `int_(4pi-2)^(4pi)(sint/2)/(4pi+2-t)dti s` `2alpha` (2) `-2alpha` (3) `alpha` (d) `-alpha`

If int_(0)^(1)(sin t)/(1+t)dx=alpha, then the value of the integral int_(4 pi-2)^(4 pi)(sin(t)/(2))/(4 pi+2-t)dt is 2 alpha(2)-2 alpha(3)alpha(d)-alpha

If int_(0)^(1)(sint)/(1+t)dt=alpha , then find the value of int_(4pi-2)^(4pi)("sin"t/2)/(4pi|2-t|)dt

If int_(0)^(1)(sint)/(1+t)dt=alpha , them the value of the integral int_(4pi-2)^(4pi)("sin"(t)/(2))/(4pi+2-t)dt in terms of alpha is given by

The value of the integral int_(0)^(pi) (xdx)/(1+cos alpha sinx), 0 lt alpha lt pi , is

The value of the integral int_(0)^(3alpha) cosec (x-alpha)cosec(x-2alpha)dx is

The value of int_(0)^((pi)/(2))sin|2x-alpha|dx, where alpha in[0,pi], is (a) 1-cos alpha(b)1+cos alpha(c)1 (d) cos alpha

The value of the integral int_(0)^(1)(dx)/(x^(2)+2xcosalpha+1) , where 0 lt alpha lt (pi)/(2) , is equal to :

If [int_0^1(dt)/(t^2+2tcosalpha+1)]x^2-[int_- 3^3(t^2sin2t)/(t^2+1)dt]x-2=0 (0 < alpha < pi) then the value of x is (i)+-sqrt((alpha)/(2sinalpha)) (ii)+-sqrt((2sinalpha)/alpha) (iii) +-sqrt(alpha/sinalpha) (iv) +-2sqrt(sinalpha/alpha)

find the value of the expression 3[sin^(4)(3(pi)/(2)-alpha)+sin^(4)(3 pi+alpha)]-2[sin^(6)((pi)/(2)+alpha)+sin^(6)(5 pi-alpha)]