`Ifint_0^(npi)f(cos^2x)dx=kint_0^pif(c0s^2x)dx ,t h e nfin dt h ev a l u ekdot`

If int_(0)^(npi) f(cos^(2)x)dx=k int_(0)^(pi) f(cos^(2)x)dx , then the value of k, is

If P = int_(0)^(3pi) f(cos^(2)x)dx and Q=int_(0)^(pi) f(cos^(2)x)dx , then

If l_(1)=int_(0)^(npi)f(|cosx|)dx and l_(2)=int_(0)^(5pi)f(|cosx|)dx , then

If kint_(0)^(1)xf(3x)dx=int_(0)^(3)tf(t)dt , then the value of k is

Statement-1: int_(0)^(npi+v)|sin x|dx=2n+1-cos v where n in N and 0 le v lt pi . Stetement-2: If f(x) is a periodic function with period T, then (i) int_(0)^(nT) f(x)dx=n int_(0)^(T) f(x)dx , where n in N and (ii) int_(nT)^(nt+a) f(x)dx=int_(0)^(a) f(x) dx , where n in N

Let f(x) be a continuous and periodic function such that f(x)=f(x+T) for all xepsilonR,Tgt0 .If int_(-2T)^(a+5T)f(x)dx=19(ag0) and int_(0)^(T)f(x)dx=2 , then find the value of int_(0)^(a)f(x)dx .

If int_(0)^(x)f(t)dt=e^(x)-ae^(2x)int_(0)^(1)f(t)e^(-t)dt , then

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