`f:(0,oo)-gtRandF(x)=int_0^xf(t)dtdotI fF(x^2)=x^2(1+x),t h e nf(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) 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 ________________

A derivable function f(x) satisfies the relation f(x)=int_(0)^(1)xf(t)dt+int_(0)^(x)x^(2)f(t)dt. The value of (2f'(1))/(f(1)) is

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f(x)=e^-xsinx , F(x)=int_0^xf(t)dt , .Find int_0^1e^x(F'(x)+f(x))dx lies in interval