[" Let "x(x)=int_(0)^(prime)f(t)dx" where "f" is such that "],[(1)/(2)<=r(t)<=b" ,or "ra(0,1]" ,and "0<=f(x)<=(1)/(3)" ,for "t" e "[1,2]],[" Then "g(2)" satisfies the inequality "]

Let f(x)=int_(0)^(1)|x-t|dt, then

Let g(x)=int_(0)^(x)f(t)dt where fis the function whose graph is shown.

If x int_(0)^(x)sin(f(t))dx=(x+2)int_(0)^(1)tsin(f(t))dt , where xgt0 , then show that f'(x)cot f(x)+3/(1+x)=0

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

Let G(x)=int e^(x)(int_(0)^(x)f(t)dt+f(x))dx where f(x) is continuous on R. If f(0)=1,G(0)=0 then G(0) equals

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

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)=int_(1)^(x)(3^(t))/(1+t^(2))dt , where xgt0 , Then

Let f(x)=int_(1)^(x)(3^(t))/(1+t^(2))dt , where xgt0 , Then