If `g(x)=int_0^xcos^4tdt ,` then `g(x+pi)` equals `g(x)+g(pi)` (b) `g(x)-g(pi)` `g(x)g(pi)` (d) `(g(x))/(g(pi))`

If g(x)=int_0^xcos^4tdt , then g(x+pi) equals (a) g(x)+g(pi) (b) g(x)-g(pi) (c) g(x)g(pi) (d) (g(x))/(g(pi))

If g(x)""=int0xcos4t"dt" , then g(x""+pi) equals: (1) g(x)/(g(pi) (2) g(x)+g(pi) (3) g(x)-g(pi) (4) g(x)dotg(pi)

If g(x)=int_(0)^(x)cos^(4)t dt, then g(x+pi) equals to (a) (g(x))/(g(pi)) (b) g(x)+g(pi) (c) g(x)-g(pi) (d) g(x).g(pi)

If g(x)=int_(0)^(x)cos^(4)t dt , then prove that g(x+pi)=g(x)+g(pi) .

If g(x)=int_0^x(|sint|+|cost|)dt ,then g(x+(pin)/2) is equal to, where n in N , (a) g(x)+g(pi) (b) g(x)+g((npi)/(2)) (c) g(x)+g(pi/2) (d) none of these

If g(x)=int_0^x(|sint|+|cost|)dt ,t h e ng(x+(pin)/2) is equal to, where n in N , a) g(x)+g(pi) (b) g(x)+ng((pi)/(n2)) c) g(x)+g(pi/2) (d) none of these

If g(x)=int_(sinx)^("sin"(2x))sin^(-1)(t)dt ,t h e n : (a) g^(prime)(pi/2)=-2pi (b) g^(prime)(-pi/2)=-2pi (c) g^(prime)(-pi/2)=2pi (d) g^(prime)(pi/2)=2pi

If g(x)=int_0^x2|t|dt ,then (a) g(x)=x|x| (b) g(x) is monotonic (c) g(x) is differentiable at x=0 (d) gprime(x) is differentiable at x=0

If g(x)=int_0^x2|t|dt ,t h e n (a) g(x)=x|x| (b) g(x) is monotonic (c) g(x) is differentiable at x=0 (d) g^(prime)(x) is differentiable at x=0

Let phi(x,t)={(x(t-1),xlet),(t(x-1), tltx):} , where t is a continuous function of x in [0,1] . Let g(x)=int_0^1 f(t)phi(x,t)dt , then g\'\'(x) = (A) g(0)+g(1)=1 (B) g(0)=0 (C) g(1)=1 (D) g\'\'(x)=f(x)