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Let $f : (0, \infty) \to R$ and let
$F (x) = \int_{0}^{x} f (t) d t$
If $F (x^{2}) = x^{2} (1 + x)$ then $f (4)$ equals

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detailed solution

Correct option is C

F(x)=∫0x f(t)dt⇒F′(x)=f(x)∴f(4)=F′(2) Also, 2xF′x2=2x(1+x)+x2⇒F′x2=1+3x/2∴f(4)=F′22=1+3=4

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Let f:(0,∞)→R and letF(x)=∫0x f(t)dtIf Fx2=x2(1+x) then f (4) equals

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Ready to Test Your Skills?

free study material

Let $f : (0, \infty) \to R$ and let
$F (x) = \int_{0}^{x} f (t) d t$
If $F (x^{2}) = x^{2} (1 + x)$ then $f (4)$ equals