Question

Let $f:(0,\infty )\to R$ and $F\left(x\right)={\int }_1^{x}f\left(t\right)dtandF\left(x^2\right)=x^2(1+x)$ then f(4) equals

• A. $\frac{5}{4}$
• B. 7
• C. 4
• D. 2

Answer 1

The correct option is C 4

$F^{{}^{\prime }}\left(x\right)=f\left(x\right)F\left(x\right)=x(1+\sqrt{x})=x+x^{3/2}\therefore F^{{}^{\prime }}\left(x\right)=f\left(x\right)=1+\frac{3}{2}\sqrt{x}\therefore f\left(4\right)=4$