If `f(a+x)=f(x),` then prove that `int_a^(n a)f(x)dx=(n-1)int_0^af(x)dx` where `a >0 and n in N.`

If f(a+x)=f(x), then prove that int_(a)^(na)f(x)dx=(n-1)int_(0)^(a)f(x)dx where a>0 and n in N.

If f is an integrable function such that f(2a-x)=f(x), then prove that int_0^(2a)f(x)dx=2int_0^af(x)dx

If f is an integrable function such that f(2a-x)=f(x), then prove that int_0^(2a)f(x)dx=2int_0^af(x)dx

If f(a+x)=f(x), then int_(0)^(na) f(x)dx is equal to (n in N)

If f(a+x)=f(x), then int_(0)^(na) f(x)dx is equal to (n in N)

If f(a+x)=f(x), then int_(0)^(na)f(x)dx is equal to n in N

Property 12:int_(a)^(a+nT)f(x)dx=n int_(0)^(T)f(x)dx where T is period of f(x)

If f(x+f(y))=f(x)+yAAx ,y in Ra n df(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dxdot

Prove that int_0^a f(x)dx=int_0^af(a-x)dx , hence evaluate int_0^pi(x sin x)/(1+cos^2 x)dx

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