Question

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

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

Answer 1

The correct option is C $4$

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