Let `f:(0,oo)rarrR` and `F(x)=int_0^x f(t)dt`. If `F(x^2)=x^2(1+x)`, then `f(4)=` (A) `5/4` (B) `7` (C) `4` (D) `2`

f:(0,oo)->R and F(x)=int_(0)^(x)f(t)dtIfF(x^(2))=x^(2)(1+x),thenf(4)

Let f:(0,oo)to R and F(x)=int_(0)^(x) f(t)dt. " If " F(x^(2))=x^(2)(1+x) , then f(4) equals

Let f : (0,oo) to R and F(x)=int_(0)^(x)t f(t)dt . If F(x^(2))=x^(4)+x^(5) , then

Let f:(0, oo) in R and F(x) = int_(0)^(x) f(t) dt . If F(x^(2))=x^(2)(1+x) then f (4) equals

Let f:(0,oo)rarr R and F(x^(3))=int_(0)^(x^(2))f(t)dt If F(x^(3))=x^(3)(x^(2)+x+1), then f(27)=

Let f:(0,oo)rarr R and F(x)=int_(0)^(x)t.f(t)dt. If F(x^(2))=x^(4)+x^(5), then sum_(r=1)^(12)f(r^(2)) equals (A) 216(B)219 (C) 221(D)225

Let :(0,oo)rarr R and F(x)=int_0^x t f(t) dt If F(x^2)=x^4+x^5,x > 0 then (i) F(4)=7 (ii) f(x) is continuous everywhere (iii) f(x) is increasing for x gt 0 (iv) f(x) is onto

Let f:(0, oo) rarr R and F(x^(2))=int_(0)^(x^(2))f(t)dt. " If "F(x^(2))=x^(2)(1+x) , then f(4) is equal to ________________

If int_0^x f(t)dt=x+int_x^1 t f(t)dt , then f(1)= (A) 1/2 (B) 0 (C) 1 (D) -1/2