If `int_(0)^(c)(bt cos4t-a sin4t)/(t^(2))dt=(a sin4x)/(x)` for all `x=0` then `4+(b)/(a)=...`

If int_(0)^(x) (bt cos 4 t - a sin 4t)/( t^(2))dt=(a sin 4x)/(x) "for all" x ne0 , then a and b are given by

If int_(0)^(t)(bx cos4x-a sin4x)/(x^(2))=(a sin4t)/(t)-1 where 0

Let int_o^x(bt cos 4t - a sin 4t)/t^2 dt = (a sin 4x)/x then a and b are given by 1) a=1/4, b = 1 2)a=2,b=2 3) a= -1, b=4 4)a=2,b=4

If int_(e)^(x) t f(t)dt=sin x-x cos x-(x^(2))/(2) for all x in R-{0} , then the value of f((pi)/(6)) will be equal to

If int_(0)^(y)cos t^(2)dt=int_(0)^(x^(2))(sin t)/(t)dt, then (dy)/(dx) is

Statement-1: int_(0)^(sin^(2)x) sin^(-1)sqrt(t dt)+int_(0)^(cos^(2)x) cos^(-1)sqrt(t dt)=(pi)/(4) for all x. Statement-2: (d)/(dx) int_(theta(x))overset(psi(x)) f(t)dt=psi'(x)f(psi(x))-psi'(x)f(psi(x))

If f(x) = int_(0)^(x)(2cos^(2)3t+3sin^(2)3t)dt , f(x+pi) is equal to :